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Elementary Algebra 2e

Review Exercises

Elementary Algebra 2eReview Exercises

Review Exercises

7.1 Greatest Common Factor and Factor by Grouping

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

363.

42 , 60 42 , 60

364.

450 , 420 450 , 420

365.

90 , 150 , 105 90 , 150 , 105

366.

60 , 294 , 630 60 , 294 , 630

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

367.

24 x 42 24 x 42

368.

35 y + 84 35 y + 84

369.

15 m 4 + 6 m 2 n 15 m 4 + 6 m 2 n

370.

24 p t 4 + 16 t 7 24 p t 4 + 16 t 7

Factor by Grouping

In the following exercises, factor by grouping.

371.

a x a y + b x b y a x a y + b x b y

372.

x 2 y x y 2 + 2 x 2 y x 2 y x y 2 + 2 x 2 y

373.

x 2 + 7 x 3 x 21 x 2 + 7 x 3 x 21

374.

4 x 2 16 x + 3 x 12 4 x 2 16 x + 3 x 12

375.

m 3 + m 2 + m + 1 m 3 + m 2 + m + 1

376.

5 x 5 y y + x 5 x 5 y y + x

7.2 Factor Trinomials of the form x2+bx+cx2+bx+c

Factor Trinomials of the Form x2+bx+cx2+bx+c

In the following exercises, factor each trinomial of the form x2+bx+cx2+bx+c.

377.

u 2 + 17 u + 72 u 2 + 17 u + 72

378.

a 2 + 14 a + 33 a 2 + 14 a + 33

379.

k 2 16 k + 60 k 2 16 k + 60

380.

r 2 11 r + 28 r 2 11 r + 28

381.

y 2 + 6 y 7 y 2 + 6 y 7

382.

m 2 + 3 m 54 m 2 + 3 m 54

383.

s 2 2 s 8 s 2 2 s 8

384.

x 2 3 x 10 x 2 3 x 10

Factor Trinomials of the Form x2+bxy+cy2x2+bxy+cy2

In the following examples, factor each trinomial of the form x2+bxy+cy2x2+bxy+cy2.

385.

x 2 + 12 x y + 35 y 2 x 2 + 12 x y + 35 y 2

386.

u 2 + 14 u v + 48 v 2 u 2 + 14 u v + 48 v 2

387.

a 2 + 4 a b 21 b 2 a 2 + 4 a b 21 b 2

388.

p 2 5 p q 36 q 2 p 2 5 p q 36 q 2

7.3 Factoring Trinomials of the form ax2+bx+cax2+bx+c

Recognize a Preliminary Strategy to Factor Polynomials Completely

In the following exercises, identify the best method to use to factor each polynomial.

389.

y 2 17 y + 42 y 2 17 y + 42

390.

12 r 2 + 32 r + 5 12 r 2 + 32 r + 5

391.

8 a 3 + 72 a 8 a 3 + 72 a

392.

4 m m n 3 n + 12 4 m m n 3 n + 12

Factor Trinomials of the Form ax2+bx+cax2+bx+c with a GCF

In the following exercises, factor completely.

393.

6 x 2 + 42 x + 60 6 x 2 + 42 x + 60

394.

8 a 2 + 32 a + 24 8 a 2 + 32 a + 24

395.

3 n 4 12 n 3 96 n 2 3 n 4 12 n 3 96 n 2

396.

5 y 3 + 25 y 2 70 y 5 y 3 + 25 y 2 70 y

Factor Trinomials Using the “ac” Method

In the following exercises, factor.

397.

2 x 2 + 9 x + 4 2 x 2 + 9 x + 4

398.

3 y 2 + 17 y + 10 3 y 2 + 17 y + 10

399.

18 a 2 9 a + 1 18 a 2 9 a + 1

400.

8 u 2 14 u + 3 8 u 2 14 u + 3

401.

15 p 2 + 2 p 8 15 p 2 + 2 p 8

402.

15 x 2 + x 2 15 x 2 + x 2

403.

40 s 2 s 6 40 s 2 s 6

404.

20 n 2 7 n 3 20 n 2 7 n 3

Factor Trinomials with a GCF Using the “ac” Method

In the following exercises, factor.

405.

3 x 2 + 3 x 36 3 x 2 + 3 x 36

406.

4 x 2 + 4 x 8 4 x 2 + 4 x 8

407.

60 y 2 85 y 25 60 y 2 85 y 25

408.

18 a 2 57 a 21 18 a 2 57 a 21

7.4 Factoring Special Products

Factor Perfect Square Trinomials

In the following exercises, factor.

409.

25 x 2 + 30 x + 9 25 x 2 + 30 x + 9

410.

16 y 2 + 72 y + 81 16 y 2 + 72 y + 81

411.

36 a 2 84 a b + 49 b 2 36 a 2 84 a b + 49 b 2

412.

64 r 2 176 r s + 121 s 2 64 r 2 176 r s + 121 s 2

413.

40 x 2 + 360 x + 810 40 x 2 + 360 x + 810

414.

75 u 2 + 180 u + 108 75 u 2 + 180 u + 108

415.

2 y 3 16 y 2 + 32 y 2 y 3 16 y 2 + 32 y

416.

5 k 3 70 k 2 + 245 k 5 k 3 70 k 2 + 245 k

Factor Differences of Squares

In the following exercises, factor.

417.

81 r 2 25 81 r 2 25

418.

49 a 2 144 49 a 2 144

419.

169 m 2 n 2 169 m 2 n 2

420.

64 x 2 y 2 64 x 2 y 2

421.

25 p 2 1 25 p 2 1

422.

1 16 s 2 1 16 s 2

423.

9 121 y 2 9 121 y 2

424.

100 k 2 81 100 k 2 81

425.

20 x 2 125 20 x 2 125

426.

18 y 2 98 18 y 2 98

427.

49 u 3 9 u 49 u 3 9 u

428.

169 n 3 n 169 n 3 n

Factor Sums and Differences of Cubes

In the following exercises, factor.

429.

a 3 125 a 3 125

430.

b 3 216 b 3 216

431.

2 m 3 + 54 2 m 3 + 54

432.

81 x 3 + 3 81 x 3 + 3

7.5 General Strategy for Factoring Polynomials

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

433.

24 x 3 + 44 x 2 24 x 3 + 44 x 2

434.

24 a 4 9 a 3 24 a 4 9 a 3

435.

16 n 2 56 m n + 49 m 2 16 n 2 56 m n + 49 m 2

436.

6 a 2 25 a 9 6 a 2 25 a 9

437.

5 r 2 + 22 r 48 5 r 2 + 22 r 48

438.

5 u 4 45 u 2 5 u 4 45 u 2

439.

n 4 81 n 4 81

440.

64 j 2 + 225 64 j 2 + 225

441.

5 x 2 + 5 x 60 5 x 2 + 5 x 60

442.

b 3 64 b 3 64

443.

m 3 + 125 m 3 + 125

444.

2 b 2 2 b c + 5 c b 5 c 2 2 b 2 2 b c + 5 c b 5 c 2

7.6 Quadratic Equations

Use the Zero Product Property

In the following exercises, solve.

445.

( a 3 ) ( a + 7 ) = 0 ( a 3 ) ( a + 7 ) = 0

446.

( b 3 ) ( b + 10 ) = 0 ( b 3 ) ( b + 10 ) = 0

447.

3 m ( 2 m 5 ) ( m + 6 ) = 0 3 m ( 2 m 5 ) ( m + 6 ) = 0

448.

7 n ( 3 n + 8 ) ( n 5 ) = 0 7 n ( 3 n + 8 ) ( n 5 ) = 0

Solve Quadratic Equations by Factoring

In the following exercises, solve.

449.

x 2 + 9 x + 20 = 0 x 2 + 9 x + 20 = 0

450.

y 2 y 72 = 0 y 2 y 72 = 0

451.

2 p 2 11 p = 40 2 p 2 11 p = 40

452.

q 3 + 3 q 2 + 2 q = 0 q 3 + 3 q 2 + 2 q = 0

453.

144 m 2 25 = 0 144 m 2 25 = 0

454.

4 n 2 = 36 4 n 2 = 36

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

455.

The product of two consecutive numbers is 462462. Find the numbers.

456.

The area of a rectangular shaped patio 400400 square feet. The length of the patio is 99 feet more than its width. Find the length and width.

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