Question

In the following exercises, factor each expression using any method${\left(x+2\right)}^2-25\left(x+2\right)-54$

Short answer

The factors are$\left(x-25\right)\left(x+4\right)$

Step-by-step solution

Step 1. Given Information

The trinomial is${\left(x+2\right)}^2-25\left(x+2\right)-54$

Find factors using substitution method

Step 2. Find the term for substitution

Rewrite the trinomial to prepare for the substitution

${\left(x+2\right)}^2-25\left(x+2\right)-54$

Substitute$x+2=u$

So, trinomial becomes$u^2-25u-54$

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

$$\begin{gathered} u^2-25u-54 \\ {u}^2-27u+2u-54 \end{gathered}$$

Factor it

$\left(u-27\right)\left(u+2\right)$

Step 4. Substitute back u

Substitute back $u=x+2$

$$\begin{gathered} \left(x+2-27\right)\left(x+2+2\right) \\ \left(x-25\right)\left(x+4\right) \end{gathered}$$