# Is it possible to factor y=x^2/2+4x+8 ? If so, what are the factors?

May 31, 2018

$y = \frac{1}{2} {\left(x + 4\right)}^{2}$

#### Explanation:

$\text{take out a "color(blue)"common factor } \frac{1}{2}$

$y = \frac{1}{2} \left({x}^{2} + 8 x + 16\right)$

${x}^{2} + 8 x + 16 \text{ is a "color(blue)"perfect square}$

$= \left(x + 4\right) \left(x + 4\right) = {\left(x + 4\right)}^{2}$

$y = \frac{1}{2} {x}^{2} + 4 x + 8 = \frac{1}{2} {\left(x + 4\right)}^{2}$