Lial - College Algebra 13th Edition

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Section R.5

Problem 81

Perform each division. See Examples 7 and 8. $(15 m^{3} + 25 m^{2} + 30 m) / (5 m^{3})$

Problem 83

Perform each division. See Examples 7 and 8. $(- 4 x^{7} - 14 x^{6} + 10 x^{4} - 14 x^{2}) / (- 2 x^{2})$

Problem 85

Perform each division. See Examples 7 and 8. $(- 4 m^{2} n^{2} - 21 m n^{3} + 18 m n^{2}) / (- 14 m^{2} n^{3})$

Problem 87

Perform each division. See Examples 7 and 8. $(8 w x y^{2} + 3 w x^{2} y + 12 w^{2} x y) / (4 w x^{2} y)$

Problem 89

Perform each division. See Examples 9 and 10. (q²+4q-32)/(q-4)

Problem 91

Perform each division. See Examples 9 and 10. (3t²+17t+10)/(3t+2)

Problem 93

Perform each division. See Examples 9 and 10. (p²+2p+20)/(p+6)

Problem 94

Perform each division. See Examples 9 and 10. (x²+11x+16)/(x+8)

Problem 97

Perform each division. See Examples 9 and 10. (4x³+9x²-10x-6)/(4x+1)

Problem 99

Perform each division. See Examples 9 and 10. (4x³-3x²+1)/(x-2)

Problem 100

Perform each division. See Examples 9 and 10.

$\frac{(3 x^{3} - 2 x + 5)}{(x - 3)}$

Problem 102

Perform each division. See Examples 9 and 10.

$\frac{(10 x^{3} + 11 x^{2} - 2 x + 3)}{(5 x + 3)}$

Problem 103

Perform each division. See Examples 9 and 10. $(x^{4} + 5 x^{2} + 5 x + 27) / (x^{2} + 3)$

Problem 104

Perform each division. See Examples 9 and 10.

$\frac{(k^{4} - 4 k^{2} + 2 k + 5)}{(k^{2} + 1)}$

Problem 114

The special products can be used to perform selected multiplications.

On the left, we use (x+y)(x-y) = x²-y². On the right, (x-y)² = x²-2xy+y².

Use special products to evaluate each expression. 63 x 57

Problem 115

The special products can be used to perform selected multiplications.

On the left, we use (x+y)(x-y) = x²-y². On the right, (x-y)² = x²-2xy+y².

Use special products to evaluate each expression. 102²

Problem 116

The special products can be used to perform selected multiplications.

On the left, we use (x+y)(x-y) = x²-y². On the right, (x-y)² = x²-2xy+y².

Use special products to evaluate each expression. 71²

Section R.6

Problem 6

Work each problem. Match each polynomial in Column I with its factored form in Column II.

Problem 7

Work each problem. Match each polynomial in Column I with its factored form in Column II.

Problem 9

Work each problem. Which of the following is the correct complete factorization of $x^{4} - 1$ ?

A. $(x^{2} - 1) (x^{2} + 1)$

B. $(x^{2} + 1) (x + 1) (x - 1)$

C. $open paren x squared minus 1 close paren squared$

D. $(x - 1)^{2} (x + 1)^{2}$

Problem 10

Work each problem. Which of the following is the correct factorization of x³+8?

A. (x+2)³

B. (x+2)(x²+2x+4)

C. (x+2)(x²-2x+4)

D. (x+2)(x²-4x+4)

Problem 11

Factor out the greatest common factor from each polynomial. See Example 1. 12m+60

Problem 13

Factor out the greatest common factor from each polynomial. See Example 1. 8k³+24k

Problem 15

Factor out the greatest common factor from each polynomial. See Example 1. xy-5xy²

Problem 16

Factor out the greatest common factor from each polynomial. See Example 1. 5h²j+hj

Problem 17

Factor out the greatest common factor from each polynomial. See Example 1. $- 4 p^{3} q^{4} - 2 p^{2} q^{5}$

Problem 19

Factor out the greatest common factor from each polynomial. See Example 1. $4 k^{2} m^{3} + 8 k^{4} m^{3} - 12 k^{2} m^{4}$

Problem 21

Factor out the greatest common factor from each polynomial. See Example 1. 2(a+b)+4m(a+b)

Problem 22

Factor out the greatest common factor from each polynomial. See Example 1. 6x(a+b)-4y(a+b)

Problem 23

Factor out the greatest common factor from each polynomial. See Example 1. (5r-6)(r+3)-(2r-1)(r+3)