Question

factor the expression.\
$n^2 - 19n + 88$\
$n^2 - 19n + 88 = \square$

Explanation:

Step1: Find pair of factors of 88

We need two numbers that multiply to $88$ and add up to $-19$. These numbers are $-8$ and $-11$, since $(-8)\times(-11)=88$ and $(-8)+(-11)=-19$.

Step2: Split middle term and factor

Rewrite the middle term using the two numbers, then factor by grouping:

$$\begin{align*} n^2 - 19n + 88&=n^2 -8n -11n +88\\ &=n(n-8)-11(n-8)\\ &=(n-8)(n-11) \end{align*}$$

Answer:

$(n-8)(n-11)$