Q. 153E - Intermediate Algebra

Question

In the following exercises, factor each expression using any method ${(x+3)}^2-9(x + 3)-36$

Step-by-Step Solution

Answer

The factors are $\left(x-9\right)\left(x+6\right)$

Step 1. Given Information

The trinomial is ${(x+3)}^2-9(x+3)-36$

Find factors using substitution method. 

Step 2. Find the term for substitution

Rewrite the trinomial to prepare for the substitution

${(x+3)}^2-9(x+3)-36$

Substitute $(x+3)=u$

So, trinomial becomes $u^2-9u-36$

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

$u^2-12u+3u-36$

Factor it

$$\begin{gathered} u\left(u-12\right)+3\left(u-12\right) \\ \left(u-12\right)\left(u+3\right) \end{gathered}$$

Step 4. Substitute back u

Substitute back $u=x+3$

$$\begin{gathered} \left(x+3-12\right)\left(x+3+3\right) \\ \left(x-9\right)\left(x+6\right) \end{gathered}$$