Question

factor $x^2 - 8x + 7$

Explanation:

Step1: Find pair summing to -8, product 7

We need two numbers that add to $-8$ and multiply to $7$. These numbers are $-1$ and $-7$.

Step2: Split middle term and factor

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

$$\begin{align*} x^2 - 8x + 7 &= x^2 - x -7x +7\\ &= x(x-1) -7(x-1)\\ &= (x-1)(x-7) \end{align*}$$

Answer:

$(x-1)(x-7)$