Lynn Marecek; MaryAnne Anthony-Smith

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.

$42, 60$

364.

$450, 420$

365.

$90, 150, 105$

366.

$60, 294, 630$

Factor the Greatest Common Factor from a Polynomial

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

367.

$24 x - 42$

368.

$35 y + 84$

369.

$15 m^{4} + 6 m^{2} n$

370.

$24 p t^{4} + 16 t^{7}$

Factor by Grouping

In the following exercises, factor by grouping.

371.

$a x - a y + b x - b y$

372.

$x^{2} y - x y^{2} + 2 x - 2 y$

373.

$x^{2} + 7 x - 3 x - 21$

374.

$4 x^{2} - 16 x + 3 x - 12$

375.

$m^{3} + m^{2} + m + 1$

376.

$5 x - 5 y - y + x$

7.2 Factor Trinomials of the form $x^{2} + b x + c$

Factor Trinomials of the Form $x^{2} + b x + c$

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .

377.

$u^{2} + 17 u + 72$

378.

$a^{2} + 14 a + 33$

379.

$k^{2} - 16 k + 60$

380.

$r^{2} - 11 r + 28$

381.

$y^{2} + 6 y - 7$

382.

$m^{2} + 3 m - 54$

383.

$s^{2} - 2 s - 8$

384.

$x^{2} - 3 x - 10$

Factor Trinomials of the Form $x^{2} + b x y + c y^{2}$

In the following examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$ .

385.

$x^{2} + 12 x y + 35 y^{2}$

386.

$u^{2} + 14 u v + 48 v^{2}$

387.

$a^{2} + 4 a b - 21 b^{2}$

388.

$p^{2} - 5 p q - 36 q^{2}$

7.3 Factoring Trinomials of the form $a x^{2} + b x + c$

Recognize a Preliminary Strategy to Factor Polynomials Completely

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

389.

$y^{2} - 17 y + 42$

390.

$12 r^{2} + 32 r + 5$

391.

$8 a^{3} + 72 a$

392.

$4 m - m n - 3 n + 12$

Factor Trinomials of the Form $a x^{2} + b x + c$ with a GCF

In the following exercises, factor completely.

393.

$6 x^{2} + 42 x + 60$

394.

$8 a^{2} + 32 a + 24$

395.

$3 n^{4} - 12 n^{3} - 96 n^{2}$

396.

$5 y^{4} + 25 y^{2} - 70 y$

Factor Trinomials Using the “ac” Method

In the following exercises, factor.

397.

$2 x^{2} + 9 x + 4$

398.

$3 y^{2} + 17 y + 10$

399.

$18 a^{2} - 9 a + 1$

400.

$8 u^{2} - 14 u + 3$

401.

$15 p^{2} + 2 p - 8$

402.

$15 x^{2} + 6 x - 2$

403.

$40 s^{2} - s - 6$

404.

$20 n^{2} - 7 n - 3$

Factor Trinomials with a GCF Using the “ac” Method

In the following exercises, factor.

405.

$3 x^{2} + 3 x - 36$

406.

$4 x^{2} + 4 x - 8$

407.

$60 y^{2} - 85 y - 25$

408.

$18 a^{2} - 57 a - 21$

7.4 Factoring Special Products

Factor Perfect Square Trinomials

In the following exercises, factor.

409.

$25 x^{2} + 30 x + 9$

410.

$16 y^{2} + 72 y + 81$

411.

$36 a^{2} - 84 a b + 49 b^{2}$

412.

$64 r^{2} - 176 r s + 121 s^{2}$

413.

$40 x^{2} + 360 x + 810$

414.

$75 u^{2} + 180 u + 108$

415.

$2 y^{3} - 16 y^{2} + 32 y$

416.

$5 k^{3} - 70 k^{2} + 245 k$

Factor Differences of Squares

In the following exercises, factor.

417.

$81 r^{2} - 25$

418.

$49 a^{2} - 144$

419.

$169 m^{2} - n^{2}$

420.

$64 x^{2} - y^{2}$

421.

$25 p^{2} - 1$

422.

$1 - 16 s^{2}$

423.

$9 - 121 y^{2}$

424.

$100 k^{2} - 81$

425.

$20 x^{2} - 125$

426.

$18 y^{2} - 98$

427.

$49 u^{3} - 9 u$

428.

$169 n^{3} - n$

Factor Sums and Differences of Cubes

In the following exercises, factor.

429.

$a^{3} - 125$

430.

$b^{3} - 216$

431.

$2 m^{3} + 54$

432.

$81 x^{3} + 3$

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.

$24 x^{3} + 44 x^{2}$

434.

$24 a^{4} - 9 a^{3}$

435.

$16 n^{2} - 56 m n + 49 m^{2}$

436.

$6 a^{2} - 25 a - 9$

437.

$5 r^{2} + 22 r - 48$

438.

$5 u^{4} - 45 u^{2}$

439.

$n^{4} - 81$

440.

$64 j^{2} + 225$

441.

$5 x^{2} + 5 x - 60$

442.

$b^{3} - 64$

443.

$m^{3} + 125$

444.

$2 b^{2} - 2 b c + 5 c b - 5 c^{2}$

7.6 Quadratic Equations

Use the Zero Product Property

In the following exercises, solve.

445.

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

446.

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

447.

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

448.

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

Solve Quadratic Equations by Factoring

In the following exercises, solve.

449.

$x^{2} + 9 x + 20 = 0$

450.

$y^{2} - y - 72 = 0$

451.

$2 p^{2} - 11 p = 40$

452.

$q^{3} + 3 q^{2} + 2 q = 0$

453.

$144 m^{2} - 25 = 0$

454.

$4 n^{2} = 36$

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

455.

The product of two consecutive numbers is $462$ . Find the numbers.

456.

The area of a rectangular shaped patio $400$ square feet. The length of the patio is $9$ feet more than its width. Find the length and width.

Review Exercises