Question

penalty: none
question
factor.
$x^2 - 12x + 32$
answer attempt 1 out of 3

Explanation:

Step1: Find pair summing to -12, product 32

We need two numbers that add up to $-12$ and multiply to $32$. These numbers are $-4$ and $-8$, since $(-4)+(-8)=-12$ and $(-4)\times(-8)=32$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, 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:

$(x-4)(x-8)$