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 as $x^2 - x -7x +7$, then factor by grouping:
$x(x-1) -7(x-1)$

Step3: Combine common factors

Factor out $(x-1)$ from both terms.

Answer:

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