# How do you factor the expression x^2 - 7x + 10?

May 16, 2018

${x}^{2} - 7 x + 10 = \left(x - 2\right) \left(x - 5\right)$

#### Explanation:

Find two numbers that multiply to $10$ and add to $- 7$.

In this case, the two numbers that work are $- 5$ and $- 2$.

Rewrite:
${x}^{2} - 7 x + 10$

$= {x}^{2} - 2 x - 5 x + 10$

$= x \left(x - 2\right) - 5 \left(x - 2\right)$

$= \left(x - 2\right) \left(x - 5\right)$