# How do you factor 5x^2 - 7x + 2?

May 25, 2015

First notice that $1$ is a root of $5 {x}^{2} - 7 x + 2 = 0$ so $\left(x - 1\right)$ is a factor.

So we can split the middle term as follows:

$5 {x}^{2} - 7 x + 2$

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

$= 5 x \left(x - 1\right) - 2 \left(x - 1\right)$

$= \left(5 x - 2\right) \left(x - 1\right)$