# How do you factor completely: 2x^2 − 28x + 98?

Jul 19, 2015

Separate out the common scalar factor, then spot a perfect square trinomial to find:

$2 {x}^{2} - 28 x + 98 = 2 \left({x}^{2} - 14 x + 49\right) = 2 {\left(x - 7\right)}^{2}$

#### Explanation:

First separate out the common scalar factor $2$ to get:

$2 {x}^{2} - 28 x + 98 = 2 \left({x}^{2} - 14 x + 49\right)$

Then note that ${x}^{2} - 14 x + 49$ is a perfect square trinomial:

It is of the form ${a}^{2} - 2 a b + {b}^{2} = {\left(a - b\right)}^{2}$ with $a = x$ and $b = 7$

So ${x}^{2} - 14 x + 49 = {x}^{2} - \left(2 \cdot x \cdot 7\right) + {7}^{2} = {\left(x - 7\right)}^{2}$