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

Answer:

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

Explanation:

Step1: Substitute $y = x^2$

$y^2 - 13y + 36$

Step2: Factor the quadratic

Find two numbers: $-4$ and $-9$ (product=36, sum=-13). So $y^2 -13y +36=(y-4)(y-9)$

Step3: Replace back $y=x^2$

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

Step4: Factor difference of squares

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

Step5: Combine factors

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