Question

How do you factor `x^6-x^4-12x^2`?

Answer 1

Given `x^6-x^4-12x^2`

Step 1: extract the obvious common factor `x^2`
`= (x^2)(x^4-x^2-12)`

Step 2: simplify the second term by temporarily substituting `t=x^2`
`=(x^2)(t^2-t-12)`
`=(x^2)(t-4)(t+3)`

Step 3: re-insert `x^2` in place of `t`
`=(x^2)(x^2-4)(x^2+3)`

Step 4: factor the middle term as the difference of squares
`=(x^2)(x+2)(x-2)(x^2+3)`