Question 1

Write   as a product of linear factors.

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Question 2

Write   in the form   when   , and demonstrate that   .

Accepted Answer

The answer of Write   in the form ...

Question 3

From the graph of the quadratic function   , determine the equation of the axis of symmetry.

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Question 4

Find all the rational zeros of the function   .

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Question 5

Using a graphing utility, graph   and approximate the zeros and their multiplicity.

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Question 6

Find two positive real numbers whose product is a maximum and whose sum is 156.

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Question 7

Match the equation with its graph.

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Question 8

Assume that y is directly proportional to x. If   and   , determine a linear model that relates y and x.

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Question 9

An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

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Question 10

Write   as a product of linear factors.

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Question 11

Given   is a root, determine all other roots of   .

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Question 12

The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d. A wire 100 meters long of diameter 5 millimeters has a resistance of 8 ohms. Find the resistance of a wire made of the same material that has a diameter of 4 millimeters and is 64 meters long.

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Question 13

Given   is a root, determine all other roots of   .

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Question 14

The simple interest on an investment is directly proportional to the amount of the investment. By investing $7750 in a certain certificate of deposit, you obtained an interest payment of $372.00 after 1 year. Determine a mathematical model that gives the interest, I , for this CD after 1 year in terms of the amount invested, P.

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Question 15

Find all real solutions of the polynomial equation   .

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Question 16

Use synthetic division to divide.

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Question 17

Use long division to divide.

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Question 18

Find all zeros of the function   .

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Question 19

If   is a root of   , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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B)    ;   
C)    ;   
D)    ;   
E)    ;   
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Question 20

Determine the x-intercept(s) of the quadratic function   .

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C)  no x-intercept(s) 
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Write as a product of linear factors.

Write in the form when , and demonstrate that .

From the graph of the quadratic function , determine the equation of the axis of symmetry.

Find all the rational zeros of the function .

Using a graphing utility, graph and approximate the zeros and their multiplicity.

Find two positive real numbers whose product is a maximum and whose sum is 156.

Match the equation with its graph.

Assume that y is directly proportional to x. If and , determine a linear model that relates y and x.

An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

Write as a product of linear factors.

Given is a root, determine all other roots of .

Given is a root, determine all other roots of .

Find all real solutions of the polynomial equation .

Use synthetic division to divide.

Use long division to divide.

Find all zeros of the function .

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Determine the x-intercept(s) of the quadratic function .

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters

Exam 4: Polynomial Functions

Write as a product of linear factors.

Write in the form when , and demonstrate that .

From the graph of the quadratic function , determine the equation of the axis of symmetry.

Find all the rational zeros of the function .

Using a graphing utility, graph and approximate the zeros and their multiplicity.

Find two positive real numbers whose product is a maximum and whose sum is 156.

Match the equation with its graph.

Assume that y is directly proportional to x. If and , determine a linear model that relates y and x.

An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

Write as a product of linear factors.

Given is a root, determine all other roots of .

Given is a root, determine all other roots of .

Find all real solutions of the polynomial equation .

Use synthetic division to divide.

Use long division to divide.

Find all zeros of the function .

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Determine the x-intercept(s) of the quadratic function .

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters