# How do you factor 5x^4+31x^2+6?

Mar 16, 2017

$5 {x}^{4} + 31 {x}^{2} + 6$

$= \left(5 {x}^{2} + 1\right) \left({x}^{2} + 6\right)$

#### Explanation:

$5 {x}^{4} + 31 {x}^{2} + 6$

Find factors of $5 \mathmr{and} 6$ whose products add to $31$

We can see that the largest product that we can find using $5 \mathmr{and} 6$ is 30, so we will not use smaller factors of $6$

$\textcolor{w h i t e}{\ldots \ldots .} 5 \mathmr{and} 6$
$\textcolor{w h i t e}{\ldots \ldots} \downarrow \text{ } \downarrow$
$\textcolor{w h i t e}{\ldots \ldots .} 5 \text{ " 1" } \rightarrow 1 \times 1 = 1$
$\textcolor{w h i t e}{\ldots \ldots .} 1 \text{ "6" } \rightarrow 5 \times 6 = \underline{30}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} 31$

The top row is the first bracket and the bottom row is the second bracket. The signs are all positive.

$5 {x}^{4} + 31 {x}^{2} + 6$

$= \left(5 {x}^{2} + 1\right) \left({x}^{2} + 6\right)$