91Ó°ÊÓ

Factor the difference of two squares. $$ 36 z^{2}-121 $$

Factor out the greatest common monomial factor from the polynomial. $$ 32 a^{5}-2 a^{3}+6 a $$

Find two consecutive positive even integers whose product is 440 .

A diver jumps from a diving board that is 32 feet above the water with an initial velocity of 16 feet per second (see figure). The height \(h\) (in feet) of the diver is modeled by the position equation $$ h=-16 t^{2}+16 t+32 $$ where \(t\) is the time measured in seconds. How long will it take for the diver to reach the water?

The fire box of a wood stove is \(x\) inches deep and \((2 x-7)\) inches wide. The volume of the fire box is \(\left(2 x^{3}-3 x^{2}-14 x\right)\) cubic inches. (a) Find the height of the fire box. (b) What is the volume of the fire box when \(x=15\) ?

Error Analysis A student submits the following steps in solving the equation \(x^{2}+4 x=12\). $$ \begin{aligned} x(x+4) &=12 \\ x &=12 \text { and } x+4=12 \\ & x = 8 \end{aligned} $$ Write an explanation of why the method does not work. Solve the equation correctly and check your solutions.

What is a prime trinomial?

In Exercises 67-74, factor the polynomial completely. $$ x^{2}-81 $$

Explain how to find the greatest common monomial factor of a binomial.

Write the prime factorization of the number. 792