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

${x}^{4} + {x}^{2} - 6 = \left({x}^{2} - 2\right) \left({x}^{2} + 3\right)$
To find this, first let $y = {x}^{2}$ to get the quadratic:
${y}^{2} + y - 6$ and factor that.
Without plugging in the general quadratic solution, just notice that ${y}^{2} + y - 6 = 0$ for $y = 2$. So $\left(y - 2\right)$ is one factor. The other factor is quickly seen to be $\left(y + 3\right)$.
Substituting $y = {x}^{2}$ back in we get the final answer.