Question

factor $x^4 - 13x^2 + 36$ completely. all factors in your answer should have integer coefficients.

Explanation:

Step1: Substitute $u=x^2$

$u^2 - 13u + 36$

Step2: Factor quadratic in $u$

Find two numbers that multiply to 36 and add to -13: -4 and -9.
$(u-4)(u-9)$

Step3: Substitute back $u=x^2$

$(x^2-4)(x^2-9)$

Step4: Factor difference of squares

$x^2-4=(x-2)(x+2)$; $x^2-9=(x-3)(x+3)$

Answer:

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