Question

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

Answer 1

`x^4 + x^2 - 6 = (x^2 - 2)(x^2 + 3)`

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 `(y - 2)` is one factor. The other factor is quickly seen to be `(y + 3)`.

Substituting `y = x^2` back in we get the final answer.