Algebra and Trigonometry (6th Edition)

Chapter 4

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Determine whether the parabola opens up or down.  ... more

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Determine whether the parabola opens up or down.  ... more

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Determine whether the parabola opens up or down.  ... more

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; Write a function that represents the product. ... more

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Dimensions: 30 feet by 30 feetMaximum area: 900 sq... more

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standardparabola ; A quadratic function is an ... more

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; You can complete the square to transform into ... more

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The value of determines which way the parabola ... more

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When a quadratic function is written in the form, ... more

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To find the -coordinate of the vertex of a ... more

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; The term "difference" means subtraction, so if ... more

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; If the length of the rectangle is and the ... more

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; When a quadratic function is written in the ... more

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; When a quadratic function is written in the ... more

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; When a quadratic function is written in the ... more

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; When a quadratic function is written in the ... more

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; The parabola in the graph has a -intercept of... more

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; Use any piece(s) of information that you can in... more

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; Use any piece(s) of information that you can in... more

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; The parabola in the graph opens downward, so ... more

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; When a quadratic function is written in the ... more

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; When a quadratic function is written in the ... more

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; When a quadratic function is written in the ... more

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; When a quadratic function is written in the ... more

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; To find the −coordinate of the vertex of a ... more

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; To find the −coordinate of the vertex of a ... more

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; To find the −coordinate of the vertex of a ... more

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; To find the −coordinate of the vertex of a ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): none-intercept: Axis of ... more

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Vertex: -intercept(s): none-intercept: Axis of ... more

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Vertex: -intercept(s): none-intercept: Axis of ... more

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Vertex: -intercept(s): none-intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): , -intercept: Axis of ... more

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Vertex: -intercept(s): none-intercept: Axis of ... more

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Vertex: -intercept(s): none-intercept: Axis of ... more

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Domain: Range:  ; Every quadratic function is a ... more

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Domain: Range: ; Every quadratic function is a ... more

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Domain: Range: ; Every quadratic function is a ... more

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Domain: Range: ; Every quadratic function is a ... more

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; When a quadratic function is written in ... more

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; When a quadratic function is written in ... more

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; When a quadratic function is written in ... more

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; When a quadratic function is written in ... more

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; First, decide which of the given functions is ... more

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; First, decide which of the given functions is ... more

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; First, decide which of the given functions is ... more

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; First, decide which of the given functions is ... more

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Number pair: and Maximum product: ; Write a ... more

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Number pair: and Maximum product: ; Write a ... more

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Number pair: and Minimum product: ; Write a ... more

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Number pair: and Minimum product: ; Write a ... more

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Dimensions: 150 ft by 300 ftMaximum area: 45,000 ... more

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Dimensions: 50 ft by 100 ftMaximum area: 5,000 sq ... more

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Dimensions: 12.5 yd by 12.5 ydMaximum area: 156.25... more

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Dimensions: 20 feet by 20 feetMaximum area: 400 sq... more

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Dimensions: 150 feet by 100 feetMaximum area: 15,... more

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Dimensions: feet by feetMaximum area: sq ft ; ... more

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Dimensions: 5 inches deep by 10 inches wideMaximum... more

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Dimensions: 3 inches deep by 6 inches wideMaximum ... more

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A quadratic function is one in which the highest ... more

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A parabola is a symmetric U-shaped curve that has ... more

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The coefficient, , of the squared term in a ... more

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When a quadratic function is written in standard ... more

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Use the formula to find the -coordinate of the ... more

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The minimum value of the parabola is 2.The ... more

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For each of the exercises you chose, enter the ... more

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Vertex: ; To find the -coordinate of the vertex, ... more

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Vertex: ; To find the -coordinate of the vertex, ... more

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Vertex: ; To find the -coordinate of the vertex, ... more

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Vertex: ; To find the -coordinate of the vertex, ... more

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It does not make sense. If the vertex of a ... more

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It makes sense. The graph of a parabola looks the ... more

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It does not make sense. If you throw something ... more

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It does not make sense. The graph looks linear ... more

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The graph of every quadratic function is a ... more

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False; The vertex of the given parabola is . ; ... more

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False; The graph has one -intercept and no -... more

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False; The maximum -value for this function is , ... more

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axis of symmetry: ; second point: ; The axis of ... more

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axis of symmetry: ; second point: ; The axis of ... more

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; Start by substituting the given vertex, , into ... more

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; Start by substituting the given vertex, , into ... more

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Dimensions: ; Maximum area: ; You need to write a ... more

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Number of trees: 65Maximum amount: 16,900 pounds... more

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No; When you solve the equation for , you get two ... more

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where ; Start by substituting and into the ... more

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; To factor a polynomial that has four terms, ... more

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; The first pair of values represents a point that... more

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even; -axis symmetry ; A function is even if . In ... more

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rises to the left and to the right ; The end ... more

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falls to the left, rises to the right ; The end ... more

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No, it would not be a good model. The leading term... more

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No, this is not a complete graph because the ... more

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and ; The zeros of a function are the value(s) of... more

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, , and ; The zeros of a function are the value(s... more

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; multiplicity 2; touches and turns ; multiplicity... more

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Since and , there is a real zero between and... more

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Falls to the left, rises to the right -intercepts... more

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Falls to the left, rises to the right   -... more

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Degree: Leading coefficient: ; The degree of a ... more

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The domain of every polynomial function is all ... more

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end; leading ; For a polynomial function, as ... more

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falls; rises ; The highest power on this function ... more

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rises; falls ; The highest power on this function ... more

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rises; rises ; The highest power on this function ... more

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falls; falls ; The highest power on this function ... more

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For a polynomial function that has an odd degree, ... more

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For a polynomial function that has an even degree... more

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-intercept ; A real zero of a polynomial function ... more

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turns around; crosses ; The multiplicity of a zero... more

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0; Intermediate Value ; The graph of every ... more

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; For a polynomial function, the maximum number ... more

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Polynomial of degree 3 ; Decide whether the ... more

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Polynomial of degree 4 ; Decide whether the ... more

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Polynomial of degree 5 ; Decide whether the ... more

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Polynomial of degree 7 ; Decide whether the ... more

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Not a polynomial ; Decide whether the function is ... more

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Not a polynomial ; Decide whether the function is ... more

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Not a polynomial ; Decide whether the function is ... more

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Not a polynomial ; Decide whether the function is ... more

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Not a polynomial ; Decide whether the function is ... more

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Polynomial of degree 2 ; Decide whether the ... more

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Polynomial ; Graphically, a polynomial function ... more

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Not a polynomial ; Graphically, a polynomial ... more

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Not a polynomial ; Graphically, a polynomial ... more

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Polynomial ; Graphically, a polynomial function ... more

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Examine the leading term. In the function given, ... more

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falls to the left, rises to the right ; The end ... more

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Falls to the left, rises to the right ; The end ... more

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rises on both ends ; The end behavior of a ... more

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rises on both ends ; The end behavior of a ... more

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falls on both ends ; The end behavior of a ... more

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falls on both ends ; The end behavior of a ... more

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; multiplicity 1; crosses; multiplicity 2; touches... more

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; multiplicity 1; crosses; multiplicity 2; touches... more

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; multiplicity 1; crosses; multiplicity 3; crosses... more

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; multiplicity 1; crosses; multiplicity 3; crosses... more

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; multiplicity 1; crosses; multiplicity 2; touches... more

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; multiplicity 1; crosses; multiplicity 2; touches... more

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The zeros are , , and 2.crosses the -axis at , , ... more

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The zeros are , , and 3.crosses the -axis at , , ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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and have opposite signs. Thus, there is a real ... more

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A polynomial function is a function with terms ... more

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The graph of a polynomial function is considered ... more

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The end behavior of a polynomial function ... more

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To determine the end behavior of a polynomial ... more

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The third-degree polynomial with a negative ... more

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The zeros of a polynomial function are the values ... more

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The graph of a polynomial function crosses the -... more

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If and of a polynomial function have opposite ... more

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The maximum number of turning points of the graph ... more

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It is possible for a polynomial function to have ... more

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It is not possible for the graph of a polynomial ... more

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Step 1: Equate , and solve for to find the -... more

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3.2.50. ; 3.2.51. ; 3.2.52. ; 3.2.53.  ; 3.2.54... more

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; Identify the behavior of the graph at both ends... more

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; Identify the behavior of the graph at both ends... more

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; Identify the behavior of the graph at both ends... more

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; Identify the behavior of the graph at both ends... more

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Instructions for TI-83:  1. Change the mode of the... more

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Instructions for TI-83:  1. Change the mode of the... more

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Instructions for TI-83:  1. Change the mode of the... more

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Instructions for TI-83:  1. Change the mode of the... more

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Instructions for TI-83:  1. Change the mode of the... more

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Instructions for TI-83:  1. Change the mode of the... more

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The statement does not make sense.  ; To determine... more

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The statement does not make sense.  ; The graph of... more

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The statement does not make sense. ; The maximum ... more

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The statement makes sense.  ; The -intercept is ... more

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The statement is false.  Replace the first "falls... more

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False, should be even (not odd) and should be ... more

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The statement is true.  ; An th-degree polynomial ... more

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False, change one of the "rise" to "fall". ; Only ... more

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; Write the factor corresponding to each given -... more

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; Write the factor corresponding to each given -... more

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year 2017 ; Let be the number of years after 1995... more

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; Simplify the inequality by multiplying by the ... more

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Point-slope form: Slope-intercept form: ; Find the... more

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; Perform the process of long division.  ; Write ... more

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; The degree of a term with one variable in a ... more

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; Factor the trinomial completely. Use the form... more

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; Arrange the polynomials by descending powers of... more

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.  ; Arrange the polynomials by descending powers ... more

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 .  ; Arrange the polynomials by descending powers... more

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The quotient is . ; Arrange the polynomials by ... more

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The answer is ; Find the remainder when is ... more

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The answer is .  ; Because is a zero of , is a ... more

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; Arrange the terms of the dividend by descending... more

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; Apply the laws of exponents when dividing the ... more

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; Divide the first term of the dividend, , by the... more

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; Divide the first term of the dividend, , by the... more

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; Divide the first term of the dividend, , by the... more

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quotientdivisorremainderdividend ; The division ... more

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; Make sure that the terms of the dividend are in... more

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; Make sure that the terms of the dividend are in... more

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true ; The degree of the result of the synthetic ... more

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; Let be the quotient and the remainder when ... more

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; Let be the quotient and the remainder when ... more

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The quotient is . ; Arrange the polynomials by ... more

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The quotient is . ; Arrange the polynomials by ... more

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The quotient is . ; Arrange the polynomials by ... more

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The quotient is . ; Arrange the polynomials by ... more

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The quotient is . ; Arrange the polynomials by ... more

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The quotient is . ; Arrange the polynomials by ... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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The quotient is . ; Arrange the polynomial by ... more

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The quotient is . ; Arrange the polynomial by ... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Arrange the polynomial by descending powers of... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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; Use synthetic division to find the remainder, ... more

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The answer is . ; Use synthetic division to ... more

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The answer is . ; Use synthetic division to ... more

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 . ; Given that is a zero of , use synthetic ... more

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 . ; Given that is a zero of , use synthetic ... more

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 . ; Given that is a zero of , use synthetic ... more

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 . ; Given that is a zero of , use synthetic ... more

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When is divided by , the remainder is 0. The ... more

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When is divided by , the remainder is 0. The ... more

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When is divided by , the remainder is 0. The ... more

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When is divided by , the remainder is 0. The ... more

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; Use synthetic division to evaluate .Copy the ... more

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; Use synthetic division to evaluate .Copy the ... more

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Step 1: Divide the first term of the dividend by ... more

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The dividend is equal to the product of the ... more

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After performing division, multiply the quotient ... more

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Step 1: Copy the coefficients of . Step 2: Bring ... more

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If a function is divided by , the remainder is ... more

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The remainder when is divided by is , while ... more

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When the remainder is zero, which is obtained by ... more

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If is a zero of , divide by using long division... more

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3.3.43.  ; 3.3.44. ; 3.3.45. ; 3.3.46. ; ... more

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The statement does not make sense. ; When is ... more

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The statement makes sense. ; When a polynomial is ... more

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The statement does not make sense.  ; Direct ... more

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The statement does not make sense.  ; Zeros of a ... more

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The statement is false; the quotient degree is 3... more

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The statement is true. ; Synthetic division is ... more

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The statement is true.  ; Synthetic division is ... more

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The statement is false. The divisor is a factor of... more

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; Obtain the remainder when is divided by , ... more

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 . ; The dividend is . The quotient is , and the ... more

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; Divide by . Use the method of long division... more

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Divide both the dividend and the divisor by 2, and... more

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The solution set is . ; Show that the remainder is... more

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Shift the graph of 3 units downward.  ; Shift the... more

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The inverse of is  ; Substitute for .  ; Replace... more

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The solution set is . ; Solve the quadratic ... more

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The solution set is . ; Solve the quadratic ... more

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; Replace with 3 and with .  ; Simplify the ... more

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The possible zeros are , , , and . ; Identify the ... more

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The possible zeros are , , , , , and . ; Identify ... more

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The solution set is . ; The leading coefficient... more

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The solution set is . ; The leading coefficient... more

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 . ; The leading coefficient, , is 1 and the ... more

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; Write the linear factorization for a third-... more

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There are 0, 2, or 4 positive real zeros, but no ... more

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constant term, leading coefficient, ; The Rational... more

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True ; The leading coefficient, , is 2, and the ... more

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False ; The leading coefficient, , is 3, and the ... more

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; The linear factorization of an th-degree ... more

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; Complex zeros always occur in pairs; if is a ... more

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; A dividend, , can be written as. The divisor is... more

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one ; For example, the linear factorization of is... more

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false  ; The number of positive real zeros is ... more

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true ; The number of positive real zeros is equal ... more

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true ; The number of positive real zeros is equal ... more

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The possible rational zeros are , ,and . ; ... more

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The possible rational zeros are , , , and . ; ... more

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The possible rational zeros are , , , , , and... more

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The possible rational zeros are , and . ; Identify... more

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The possible rational zeros are , and . ; Identify... more

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The possible rational zeros are , and . ; Identify... more

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The possible rational zeros are , and . ; Identify... more

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The possible rational zeros are , and . ; Identify... more

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; Write the linear factorization for a third-... more

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; Write the linear factorization for a third-... more

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; Write the linear factorization for a third-... more

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; Write the linear factorization for a third-... more

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; Write the linear factorization for a fourth-... more

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; Write the linear factorization for a fourth-... more

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; Write the linear factorization for a fourth-... more

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; Write the linear factorization for a fourth-... more

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The function has no positive real roots, but has 3... more

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The function has no positive real roots, but has 3... more

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The function has 3 or 1 positive real roots but no... more

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The function has 3 or 1 positive real roots but no... more

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The function has 2 or 0 positive real roots and 2 ... more

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The function has 3 or 1 positive real roots and 1 ... more

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The zeros of the function as , 1, and 5. ; Find ... more

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The zeros of the function are and (multiplicity ... more

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The roots are , , and . ; Find all possible ... more

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The roots are , , and . ; Find all possible ... more

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The zeros are (multiplicity 1), , and . ; Find ... more

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The zeros are (multiplicity 2), , and . ; Find ... more

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The roots are , , , and . ; Find all possible ... more

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The roots are , 2, , and .  ; Find all possible ... more

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The zeros are , , 2, and 3. ; Find all possible ... more

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The zeros are , 1, , and . ; Find all possible ... more

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The roots are 1, , , and . ; Find all possible ... more

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The roots are 4, , , and . ; Find all possible ... more

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The roots are (multiplicity 2), , , and . ; Find ... more

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The roots are , , , , and 3. ; Find all possible ... more

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Two possibilities are 10 inches and inches. ; ... more

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Two possibilities are 5 inches and inches. ; ... more

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Use the formula . ; From the given function, , ... more

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The number of zeros of a polynomial function, , is... more

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The number of positive real zeros of a polynomial ... more

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The number of negative real zeros of a polynomial ... more

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When one of the roots of a third-degree equation ... more

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The roots of are complex numbers. ; Let . The ... more

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The leading coefficient is a multiple of 4 and the... more

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Find all possible rational roots of the equation, ... more

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Find all possible rational roots of the equation, ... more

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Find all possible rational roots of the equation, ... more

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Find all possible rational roots of the equation, ... more

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The graph of does not have any real roots. ; ... more

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The graph of does not cross the -axis on the ... more

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It is not possible for an odd-degree polynomial ... more

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has one real root and 2 imaginary roots. ; Graph .... more

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The graph of has 3 real roots and 2 imaginary ... more

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The graph of has 2 real roots and 2 imaginary ... more

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The graph of has 2 real roots and 4 imaginary ... more

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The statement makes sense. ; To determine the ... more

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The statement does not make sense. ; The quadratic... more

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The statement makes sense. ; Because is a zero of... more

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The statement makes sense. ; has four possible ... more

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The statement is false; the equation has no ... more

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The statement is false; it does not give the exact... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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; Arrange the polynomials by descending powers of... more

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,,, ,,,, and . ; Identify the leading coefficient... more

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There are 2 or 0 positive real zeros, but no ... more

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; ; Find the possible rational zeros, where the ... more

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There are four real zeros, and one zero has ... more

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There are three real zeros, and 2 imaginary zeros... more

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There are two real zeros, and two imaginary zeros... more

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There is one real zero, and four imaginary zeros... more

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Graph , with a vertical asymptote at and ... more

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Graph , with a vertical asymptote at and ... more

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Simplify if the numerator, , and the denominator... more

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Simplify if the numerator, , and the denominator... more

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Simplify if the numerator, , and the denominator... more

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The horizontal asymptote is . The number of ... more

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The horizontal asymptote is . The more years of ... more

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; Since the right side of the inequality is zero... more

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134.4 cubic centimeters ; Write the equation given... more

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1600 feet ; Write the equation given the ... more

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440 vps ; Write the equation given the information... more

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112 db ; Write the equation given the information... more

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800 cubic feet ; Write the equation given the ... more

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Axis of symmetry: Domain: all real numbersRange... more

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23 units; highest profit: ; The function is ... more

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Domain: ; A rational function is defined for all ... more

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Domain: ; A rational function is defined for all ... more

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Domain: ; A rational function is defined for all ... more

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Domain: ; A rational function is defined for all ... more

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; Rewrite the inequality such that the right side... more

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45 foot-candles ; Write the equation given the ... more

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with multiplicity 2; 1 with multiplicity 2.  ; The... more

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3 ; By counting the ticks in the graph, is zero ... more

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