Lynn Marecek

Practice Test

In the following exercises, factor completely.

445.

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

446.

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

447.

$x^{2} + 13 x + 36$

448.

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

449.

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

450.

$40 r^{2} + 810$

451.

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

452.

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

453.

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

454.

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

455.

$x^{3} + 125$

456.

$32 x^{5} y^{2} - 162 x y^{2}$

457.

$6 x^{4} - 19 x^{2} + 15$

458.

$3 x^{3} - 36 x^{2} + 108 x$

In the following exercises, solve

459.

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

460.

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

461.

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 placemat.

462.

Jing is going to throw a ball from the balcony of her condo. When she throws the ball from 80 feet above the ground, the function $h (t) = −16 t^{2} + 64 t + 80$ models the height, h, of the ball above the ground as a function of time, t. Find: ⓐ the zeros of this function which tells us when the ball will hit the ground. ⓑ the time(s) the ball will be 128 feet above the ground. ⓒ the height the ball will be at $t = 4$ seconds.

463.

For the function, $f (x) = x^{2} - 7 x + 5,$ ⓐ find when $f (x) = −7$ ⓑ Use this information to find two points that lie on the graph of the function.

464.

For the function $f (x) = 25 x^{2} - 81,$ find: ⓐ the zeros of the function ⓑ the x-intercepts of the graph of the function ⓒ the y-intercept of the graph of the function.