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

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Answer 1 · 2015-05-25T18:36:59

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
$=(x^2)(x+2)(x-2)(x^2+3)$

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