Question

factor: $x^2 + 12x + 32$

Explanation:

Step1: Find pair summing to 12, product 32

The pair is 4 and 8, since $4+8=12$ and $4\times8=32$.

Step2: Split middle term and factor

Rewrite the polynomial, then factor by grouping:

$$\begin{align*} x^2+12x+32&=x^2+4x+8x+32\\ &=x(x+4)+8(x+4)\\ &=(x+4)(x+8) \end{align*}$$

Answer:

$(x+4)(x+8)$