Question

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

Explanation:

Step1: Find pair summing to -19, product 88

We need two numbers that add to $-19$ and multiply to $88$. These numbers are $-8$ and $-11$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, 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:

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