Practice Test

In the following exercises, find the Greatest Common Factor in each expression.

457.

$14 y - 42$

458.

$−6 x^{2} - 30 x$

459.

$80 a^{2} + 120 a^{3}$

460.

$5 m (m - 1) + 3 (m - 1)$

In the following exercises, factor completely.

461.

$x^{2} + 13 x + 42$

462.

$p^{2} + p q - 12 q^{2}$

463.

$3 a^{3} - 6 a^{2} - 72 a$

464.

$s^{2} - 25 s + 84$

465.

$5 n^{2} + 30 n + 45$

466.

$64 y^{2} - 49$

467.

$x y - 8 y + 7 x - 56$

468.

$40 r^{2} + 810$

469.

$9 s^{2} - 12 s + 4$

470.

$n^{2} + 12 n + 36$

471.

$100 - a^{2}$

472.

$6 x^{2} - 11 x - 10$

473.

$3 x^{2} - 75 y^{2}$

474.

$c^{3} - 1000 d^{3}$

475.

$a b - 3 b - 2 a + 6$

476.

$6 u^{2} + 3 u - 18$

477.

$8 m^{2} + 22 m + 5$

In the following exercises, solve.

478.

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

479.

$y^{2} = y + 132$

480.

$5 a^{2} + 26 a = 24$

481.

$9 b^{2} - 9 = 0$

482.

$16 - m^{2} = 0$

483.

$4 n^{2} + 19 n + 21 = 0$

484.

$(x - 3) (x + 2) = 6$

485.

The product of two consecutive integers is 156. Find the integers.

486.

The area of a rectangular place mat is $168$ square inches. Its length is two inches longer than the width. Find the length and width of the place mat.