# How do you factor y=5x^4+10x^2-15 ?

Mar 2, 2016

First factor you can take out is $5$

#### Explanation:

$= 5 \left({x}^{4} + 2 {x}^{2} - 3\right)$

Now if you see ${x}^{2}$ as a whole (let's call ${x}^{2} = z$ just for now) you have a quadratic expression you can factor further:
$= 5 \left({z}^{2} + 2 z - 3\right) = 5 \left(z + 3\right) \left(z - 1\right)$

Translated back, this becomes:
$= 5 \left({x}^{2} + 3\right) \left({x}^{2} - 1\right)$

And you can factor the last term even further:
$= 5 \left({x}^{2} + 3\right) \left(x - 1\right) \left(x + 1\right)$