Question

factor.
$w^{2}+18w + 17$

Explanation:

Step1: Find pair summing to 18, product 17

We need two numbers that add up to 18 and multiply to 17. These numbers are 1 and 17, since $1+17=18$ and $1\times17=17$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, then factor by grouping:

$$\begin{align*} w^2 + 18w + 17 &= w^2 + w + 17w + 17\\ &= w(w+1) + 17(w+1)\\ &= (w+1)(w+17) \end{align*}$$

Answer:

$(w+1)(w+17)$