### Practice Test

In the following exercises, factor completely.

$5m\left(m-1\right)+3\left(m-1\right)$

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

$40{r}^{2}+810$

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

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

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

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

In the following exercises, solve

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

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.

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 $h\left(t\right)=\mathrm{-16}{t}^{2}+64t+80$ 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.

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

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