Quiz 3: Polynomial and Rational Functions

Graph the given function. A) B) C) D) E)

Determine the vertex of the graph of the quadratic function . A) B) C) D) E)

Find the standard form of the quadratic function shown below: A) B) C) D) E)

Write the standard form of the equation of the parabola that has a vertex at and passes through the point . A) B) C) D) E)

Write the standard form of the equation of the parabola that has a vertex at and passes through the point . A) B) C) D) E)

A farmer has 240 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. A) B) C) D) E)

Find all real zeros of the polynomial and determine the multiplicity of each. A) B) C) D) E)

Find all real zeros of the polynomial and determine the multiplicity of each. A) B) C) D) E)

Using a graphing utility, graph and approximate the zeros and their multiplicity. A) B) C) D) E)

An open box is to be made from a square piece of cardboard, 35 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. A) B) C) D) E)

Use long division to divide. A) B) 4x - 1 C) D) E)

Use synthetic division to divide. A) B) C) D) E)

Write in the form when . A) B) C) D) E)

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation. A) ; B) ; C) ; D) ; E) ;

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form. A) B) C) D) E)

Find all the rational zeros of the function . A) B) C) D) E)

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of . A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real B) 3 positive reals or 1 positive real; no negative reals C) no positive reals; no negative reals D) 3 positive reals or 1 positive real; 1 negative real E) 1 positive real; 3 negative reals or 1 negative real

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of . A) 3 positive reals or 1 positive real; no negative reals B) no positive reals; no negative reals C) 1 positive real; 3 negative reals or 1 negative real D) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real E) 0 positive real; 3 negative reals or 1 negative real

Find all the real zeros of . A) B) C) D) E)

Find all the real zeros of . A) B) C) D) E)

Find all zeros of the function . A) B) C) D) E)

Find all zeros of the function . A) B) C) D) E)

Write as a product of linear factors. A) B) C) D) E)

Write as a product of linear factors. A) B) C) D) E)

Determine the zeros (if any) of the rational function . A) B) C) no zeros D) E)

Graph the given function. A) B) C) D) E)

Determine the vertex of the graph of the quadratic function . A) B) C) D) E)

Find the standard form of the quadratic function shown below: A) B) C) D) E)

Write the standard form of the equation of the parabola that has a vertex at and passes through the point . A) B) C) D) E)

Write the standard form of the equation of the parabola that has a vertex at and passes through the point . A) B) C) D) E)

A farmer has 240 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. A) B) C) D) E)

Find all real zeros of the polynomial and determine the multiplicity of each. A) B) C) D) E)

Find all real zeros of the polynomial and determine the multiplicity of each. A) B) C) D) E)

Using a graphing utility, graph and approximate the zeros and their multiplicity. A) B) C) D) E)

An open box is to be made from a square piece of cardboard, 35 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. A) B) C) D) E)

Use long division to divide. A) B) C) D) E) 4x - 3

Use synthetic division to divide. A) B) C) D) E)

Write in the form when . A) B) C) D) E)

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation. A) ; B) ; C) ; D) ; E) ;

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form. A) B) C) D) E)

Find all the rational zeros of the function . A) B) C) D) E)

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of . A) 3 positive reals or 1 positive real; 1 negative real B) 3 positive reals or 1 positive real; no negative reals C) no positive reals; no negative reals D) 1 positive real; 3 negative reals or 1 negative real E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of . A) 3 positive reals or 1 positive real; no negative reals B) 1 positive real; 3 negative reals or 1 negative real C) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real D) no positive reals; no negative reals E) 0 positive real; 3 negative reals or 1 negative real

Find all the real zeros of . A) B) C) D) E)

Find all the real zeros of . A) B) C) D) E)

Find all zeros of the function . A) B) C) D) E)

Find all zeros of the function . A) B) C) D) E)

Write as a product of linear factors. A) B) C) D) E)

Write as a product of linear factors. A) B) C) D) E)

Determine the zeros (if any) of the rational function . A) no zeros B) C) D) E)

Graph the given function. A) B) C) D) E)

Determine the vertex of the graph of the quadratic function . A) B) C) D) E)

Find the standard form of the quadratic function shown below: A) B) C) D) E)

Write the standard form of the equation of the parabola that has a vertex at and passes through the point . A) B) C) D) E)

Write the standard form of the equation of the parabola that has a vertex at and passes through the point . A) B) C) D) E)

A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. A) B) C) D) E)

Find all real zeros of the polynomial and determine the multiplicity of each. A) B) C) D) E)

Find all real zeros of the polynomial and determine the multiplicity of each. A) B) C) D) E)

Using a graphing utility, graph and approximate the zeros and their multiplicity. A) B) C) D) E)

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. A) B) C) D) E)

Use long division to divide. A) B) C) D) E) -x + 2

Use synthetic division to divide. A) B) C) D) E)

Write in the form when . A) B) C) D) E)

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation. A) ; B) ; C) ; D) ; E) ;

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form. A) B) C) D) E)

Find all the rational zeros of the function . A) B) C) D) E)

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of . A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real B) 3 positive reals or 1 positive real; no negative reals C) 1 positive real; 3 negative reals or 1 negative real D) 3 positive reals or 1 positive real; 1 negative real E) no positive reals; no negative reals

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of . A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real B) 3 positive reals or 1 positive real; no negative reals C) 0 positive real; 3 negative reals or 1 negative real D) 1 positive real; 3 negative reals or 1 negative real E) no positive reals; no negative reals

Find all the real zeros of . A) B) C) D) E)

Find all the real zeros of . A) B) C) D) E)

Find all zeros of the function . A) B) C) D) E)

Find all zeros of the function . A) B) C) D) E)

Write as a product of linear factors. A) B) C) D) E)

Write as a product of linear factors. A) B) C) D) E)

Determine the zeros (if any) of the rational function . A) B) C) D) E) no zeros

Graph the quadratic function. f (x) = - 3x² + 2 A) C) C) D)

Graph the quadratic function. f (x) = x² + 3x A) C) C) D)

Find the vertex of the parabola. y = 9x² - 10 A) (0, -10) B) (0, 9) C) (9, -10) D) (-10, 0) E) (-10, 9)

Graph the quadratic function. A) C) C) D)

Find the vertex of the parabolic graph of the equation. y = 6(x - 7) ² + 4 A) (49, 4) B) (7, 6) C) (4, 7) D) (7, 4) E) (7, 0)

Find the vertex of the parabola. y = x² - 14x + 49 A) (7, 0) B) (7, -35) C) (0, 7) D) (49, 0) E) (-35, 0)

Graph the quadratic function. f (x) = - x² - 3x + 2 A) C) C) D)

Tell whether the function is even or odd. If it is neither, so indicate. A) even B) odd C) neither

The graph of the function g(x) is a translation of the graph of f (x) = x ³. Graph the function g(x) = (x - 2) ³. A) C) C) D)

Graph the polynomial function. A) C) C) D)

The graph of the function g(x) is a translation of the graph of f (x) = x ³. Graph the function g(x) = (x - 5) ³ - 2. A) C) C) D)

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Use synthetic division to express in the form for the divisor . A) B) C) D) E) none of these

Let . Use synthetic division to find the value . A) B) C) D) E) none of these

Use synthetic division to perform the division. A) B) C) D) E) none of these

Do the operation and express the answer in a + bi form. (8 - 7 i) + (9 + 5 i) A) 17 + 2 i B) - 17 - 2 i C) - 17 + 2 i D) 2 - 17 i E) 17 - 2 i

Do the operation and express the answer in a + bi form. A) 11 - 7 i B) - 11 - 7 i C) - 11 + 14 i D) - 11 + 7 i E) 11 + 7 i

Do the operation and express the answer in a + bi form. A) - 27 + 3 i B) 27 - 3 i C) - 3 + 3 i D) 3 - 3 i E) 27 + 3 i

Do the operation and express the answer in a + bi form. A) - 100 i B) 10 i C) - 10 i D) 10 E) - 10

Simplify the expression. i ^-6 A) - 1 B) - i C) - 3i D) 1 E) i

Do the operation and express the answer in a + bi form. A) - 9 i B) - 9 C) 9 i D) - 45 i E) 9

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Graph the function A) C) C) D)

Graph the function. A) C) C) D)

Graph the quadratic function. f (x) = - 4x² + 2 A) C) C) D)

Graph the quadratic function. f (x) = x² + 2x A) C) C) D)

Find the vertex of the parabola. y = 6x² - 4 A) (0, -4) B) (-4, 0) C) (0, 6) D) (6, -4) E) (-4, 6)

Graph the quadratic function. A) C) C) D)

Find the vertex of the parabolic graph of the equation. y = 6(x - 5) ² + 1 A) (25, 1) B) (1, 5) C) (5, 1) D) (5, 0) E) (5, 6)

Find the vertex of the parabola. y = x² - 18x + 81 A) (0, 9) B) (81, 0) C) (9, 0) D) (9, -63) E) (-63, 0)

Graph the quadratic function. f (x) = - x² - 4x + 4 A) C) C) D)

Tell whether the function is even or odd. If it is neither, so indicate. A) odd B) even C) neither

The graph of the function g(x) is a translation of the graph of f (x) = x ³. Graph the function g(x) = (x - 2) ³. A) C) C) D)

Graph the polynomial function. A) C) C) D)

The graph of the function g(x) is a translation of the graph of f (x) = x ³. Graph the function g(x) = (x - 3) ³ - 1. A) C) C) D)

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Use synthetic division to express in the form for the divisor . A) B) C) D) E) none of these

Let . Use synthetic division to find the value . A) B) C) D) E) none of these

Use synthetic division to perform the division. A) B) C) D) E) none of these

Do the operation and express the answer in a + bi form. (9 - 10 i) + (2 + 3 i) A) 11 - 7 i B) 11 + 7 i C) - 11 + 7 i D) 7 - 11 i E) - 11 - 7 i

Do the operation and express the answer in a + bi form. A) - 13 - 11 i B) - 13 + 11 i C) 13 + 11 i D) - 13 + 22 i E) 13 - 11 i

Do the operation and express the answer in a + bi form. A) 16 + 11 i B) - 2 + 11 i C) 16 - 2 i D) 2 - 11 i E) - 16 + 11 i

Do the operation and express the answer in a + bi form. A) - 19 i B) - 19 C) - 190 i D) 19 E) 19 i

Simplify the expression. i ^-2 A) - i B) - 1 C) i D) - 3i E) 1

Do the operation and express the answer in a + bi form. A) - 15 i B) - 3 i C) 3 D) 3 i E) - 3

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Graph the function A) C) C) D)

Graph the function. A) C) C) D)

Graph the quadratic function. f (x) = - 4x² + 2 A) C) C) D)

Graph the quadratic function. f (x) = x² + 3x A) C) C) D)

Find the vertex of the parabola. y = 6x² - 2 A) (-2, 6) B) (0, -2) C) (6, -2) D) (-2, 0) E) (0, 6)

Graph the quadratic function. A) C) C) D)

Find the vertex of the parabolic graph of the equation. y = 5(x - 8) ² + 4 A) (8, 0) B) (64, 4) C) (8, 5) D) (4, 8) E) (8, 4)

Find the vertex of the parabola. y = x² - 6x + 9 A) (-3, 0) B) (3, 0) C) (0, 3) D) (9, 0) E) (3, -3)

Graph the quadratic function. f (x) = - x² - 3x + 2 A) C) C) D)

Tell whether the function is even or odd. If it is neither, so indicate. A) even B) odd C) neither

The graph of the function g(x) is a translation of the graph of f (x) = x ³. Graph the function g(x) = (x - 1) ³. A) C) C) D)

Graph the polynomial function. A) C) C) D)

The graph of the function g(x) is a translation of the graph of f (x) = x ³. Graph the function g(x) = (x - 3) ³ - 1. A) C) C) D)

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Use synthetic division to express in the form for the divisor . A) B) C) D) E) none of these

Let . Use synthetic division to find the value . A) B) C) D) E) none of these

Use synthetic division to perform the division. A) B) C) D) E) none of these

Do the operation and express the answer in a + bi form. (8 - 10 i) + (5 + 7 i) A) 3 - 13 i B) - 13 + 3 i C) 13 + 3 i D) - 13 - 3 i E) 13 - 3 i

Do the operation and express the answer in a + bi form. A) - 11 + 18 i B) 11 + 9 i C) - 11 + 9 i D) - 11 - 9 i E) 11 - 9 i

Do the operation and express the answer in a + bi form. A) 16 - 3 i B) - 16 + 2 i C) - 3 + 2 i D) 3 - 2 i E) 16 + 2 i

Do the operation and express the answer in a + bi form. A) 19 i B) - 19 i C) - 190 i D) - 19 E) 19

Simplify the expression. i ^-6 A) i B) - 3i C) - i D) - 1 E) 1

Do the operation and express the answer in a + bi form. A) - 8 i B) - 40 i C) - 8 D) 8 i E) 8

Find a polynomial with the given zeros. A) B) C) D) E) none of these

Graph the function A) C) C) D)

Graph the function. A) C) C) D)