Solution: In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use

For the function f 1x2 = x4 - 6x3 + x2 + 24x - 20, use long division to determine whether each of the following is a factor of f 1x2.

For the function h1x2 = x3 - x2 - 17x - 15, use long division to determine whether each of the following is a factor of h1x2. a) x + 5 b) x + 1 c) x + 3

For the function g1x2 = x3 - 2x2 - 11x + 12, use long division to determine whether each of the following is a factor of g1x2. a) x - 4 b) x - 3 c) x - 1

For the function f 1x2 = x4 + 8x3 + 5x2 - 38x + 24, use long division to determine whether each of the following is a factor of f 1x2. a) x + 6 b) x + 1 c) x - 4

In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use long division to find the quotient Q1x2 and the remainder R1x2 when P1x2 is divided by d1x2. Express P1x2 in the form d1x2 Q1x2 + R1x2.P1x2 = x3 - 8, d1x2 = x + 2

In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use long division to find the quotient Q1x2 and the remainder R1x2 when P1x2 is divided by d1x2. Express P1x2 in the form d1x2 Q1x2 + R1x2.P1x2 = 2x3 - 3x2 + x - 1, d1x2 = x - 3

In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use long division to find the quotient Q1x2 and the remainder R1x2 when P1x2 is divided by d1x2. Express P1x2 in the form d1x2 Q1x2 + R1x2.P1x2 = x3 + 6x2 - 25x + 18, d1x2 = x + 9

In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use long division to find the quotient Q1x2 and the remainder R1x2 when P1x2 is divided by d1x2. Express P1x2 in the form d1x2 Q1x2 + R1x2.P1x2 = x3 - 9x2 + 15x + 25, d1x2 = x - 5

In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use long division to find the quotient Q1x2 and the remainder R1x2 when P1x2 is divided by d1x2. Express P1x2 in the form d1x2 Q1x2 + R1x2.P1x2 = x4 - 2x2 + 3, d1x2 = x + 2

In each of the following, a polynomial P1x2 and a divisor d1x2 are given. Use long division to find the quotient Q1x2 and the remainder R1x2 when P1x2 is divided by d1x2. Express P1x2 in the form d1x2 Q1x2 + R1x2.P1x2 = x4 + 6x3 , d1x2 = x - 1

Use synthetic division to find the quotient and the remainder.12x4 + 7x3 + x - 122 , 1x + 32

Use synthetic division to find the quotient and the remainder. 1x3 - 7x2 + 13x + 32 , 1x - 22

Use synthetic division to find the quotient and the remainder.1x3 - 2x2 - 82 , 1x + 22

Use synthetic division to find the quotient and the remainder.1x3 - 3x + 102 , 1x - 22

Use synthetic division to find the quotient and the remainder.13x3 - x2 + 4x - 102 , 1x + 12

Use synthetic division to find the quotient and the remainder.14x4 - 2x + 52 , 1x + 32

Use synthetic division to find the quotient and the remainder.1x5 + x3 - x2 , 1x - 32

Use synthetic division to find the quotient and the remainder.1x7 - x6 + x5 - x4 + 22 , 1x + 12

Use synthetic division to find the quotient and the remainder.1x4 - 12 , 1x - 12

Use synthetic division to find the quotient and the remainder.1x5 + 322 , 1x + 22

Use synthetic division to find the quotient and the remainder.12x4 + 3x2 - 12 , 1x - 1 2 2

Use synthetic division to find the quotient and the remainder.13x4 - 2x2 + 22 , 1x - 1 4 2

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = x3 - 6x2 + 11x - 6; find f 112, f 1-22, and f 132.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = x3 + 7x2 - 12x - 3; find f 1-32, f 1-22, and f 112.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = x4 - 3x3 + 2x + 8; find f 1-12, f 142, and f 1-52.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = 2x4 + x2 - 10x + 1; find f 1-102, f 122, and f 132.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = 2x5 - 3x4 + 2x3 - x + 8; find f 1202 and f 1-32.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = x5 - 10x4 + 20x3 - 5x - 100; find f 1-102 and f 152.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = x4 - 16; find f 122, f 1-22, f 132, and f 11 - 22 2.

Use synthetic division to find the function values. Then check your work using a graphing calculatorf 1x2 = x5 + 32; find f 122, f 1-22, f 132, and f 12 + 3i2.

Using synthetic division, determine whether the numbers are zeros of the polynomial function.-3, 2; f 1x2 = 3x3 + 5x2 - 6x + 18

Using synthetic division, determine whether the numbers are zeros of the polynomial function.-4, 2; f 1x2 = 3x3 + 11x2 - 2x + 8

Using synthetic division, determine whether the numbers are zeros of the polynomial function.-3, 1; h1x2 = x4 + 4x3 + 2x2 - 4x - 3

Using synthetic division, determine whether the numbers are zeros of the polynomial function.2, -1; g1x2 = x4 - 6x3 + x2 + 24x - 20

Using synthetic division, determine whether the numbers are zeros of the polynomial function. i, -2i; g1x2 = x3 - 4x2 + 4x - 16

Using synthetic division, determine whether the numbers are zeros of the polynomial function.1 3, 2; h1x2 = x3 - x2 - 1 9 x + 1 9

Using synthetic division, determine whether the numbers are zeros of the polynomial function.-3, 1 2; f 1x2 = x3 - 7 2 x2 + x - 3 2

Using synthetic division, determine whether the numbers are zeros of the polynomial function.i, -i, -2; f 1x2 = x3 + 2x2 + x + 2

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x3 + 4x2 + x - 6

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x3 + 5x2 - 2x - 24

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x3 - 6x2 + 3x + 10

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x3 + 2x2 - 13x + 10

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x3 - x2 - 14x + 24

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x3 - 3x2 - 10x + 24

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x4 - 7x3 + 9x2 + 27x - 54

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x4 - 4x3 - 7x2 + 34x - 24

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x4 - x3 - 19x2 + 49x - 30

Factor the polynomial function f 1x2. Then solve the equation f 1x2 = 0.f 1x2 = x4 + 11x3 + 41x2 + 61x + 30

Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros.f 1x2 = x4 - x3 - 7x2 + x + 6

Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros.f 1x2 = x4 + x3 - 3x2 - 5x - 2

Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros.f 1x2 = x3 - 7x + 6

Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros.f 1x2 = x3 - 12x + 16

Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros.f 1x2 = -x3 + 3x2 + 6x - 8

Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros.f 1x2 = -x4 + 2x3 + 3x2 - 4x - 4

Solve. Find exact solutions.2x2 + 12 = 5x

Solve. Find exact solutions.7x2 + 4x = 3

In Exercises 5759, consider the function g1x2 = x2 + 5x - 14.What are the inputs if the output is -14?

In Exercises 5759, consider the function g1x2 = x2 + 5x - 14.What is the output if the input is 3?

In Exercises 5759, consider the function g1x2 = x2 + 5x - 14.Given an output of -20, find the corresponding inputs.

Movie Ticket Prices. The average price of a movie ticket has increased linearly over the years, rising from $5.39 in 2000 to $7.89 in 2010 (Source: National Association of Theatre Owners). Using these two data points, find a linear function, f 1x2 = mx + b, that models the data. Let x represent the number of years since 2000. Then use this function to estimate the average price of a movie ticket in 2005 and in 2015.

The sum of the base and the height of a triangle is 30 in. Find the dimensions for which the area is a maximum.

In Exercises 62 and 63, a graph of a polynomial function is given. On the basis of the graph:

In Exercises 62 and 63, a graph of a polynomial function is given. On the basis of the graph:

For what values of k will the remainder be the same when x2 + kx + 4 is divided by x - 1 and by x + 1?

Find k such that x + 2 is a factor of x3 - kx2 + 3x + 7k.

Beam Deflection. A beam rests at two points A and B and has a concentrated load applied to its center. Let y = the deflection, in feet, of the beam at a distance of x feet from A. Under certain conditions, this deflection is given by y = 1 13 x3 - 1 14 x.

Solve.2x2 x2 - 1 + 4 x + 3 = 12x - 4 x3 + 3x2 - x - 3

Solve.6x2 x2 + 11 + 60 x3 - 7x2 + 11x - 77 = 1 x - 7

Find a 15th-degree polynomial for which x - 1 is a factor. Answers may vary.

Use synthetic division to divide. 1x4 - y 4 2 , 1x - y2

Use synthetic division to divide.1x3 + 3ix2 - 4ix - 22 , 1x + i2

Use synthetic division to divide.1x2 - 4x - 22 , 3x - 13 + 2i24

Use synthetic division to divide.1x2 - 3x + 72 , 1x - i2