Question

factor.
$g^2 + 18g + 17$

Explanation:

Step1: Find pair summing to 18, product 17

We need two numbers that add to 18 and multiply to 17: 1 and 17.

Step2: Split middle term and factor

Rewrite the quadratic as $g^2 + g + 17g + 17$, then group and factor:

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

Answer:

$(g+1)(g+17)$