Question

How do you factor completely `x^4 - 13x^2 + 36`?

Answer 1

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

Explanation:

Call x^2 = X, and factor the bi-quadratic trinomial:
x^2 - 13X + 36
Find 2 numbers knowing sum (-13) and product (36). They are (-4, -9).
y = (X - 4)(X - 9)
Replace X by x^2 -->
y = (x^2 - 4)(x^2 - 9)
y = (x - 2)(x + 2)( x - 3)(x + 3)