Question

Factorize:
x^4 - 6x^2 - 27​

Answer 1

x^4 - 6x^2 - 27

Let u = x^2

We know that x^4 = (x^2)^2.

u^2 - 6u - 27

(u - 9)(u + 3)

Now, back-substitite for u.

(x^2 - 9)(x^2 + 3)

The RIGHT SIDE FACTOR is the difference of two squares.

So, x^2 - 9 becomes (x - 3)(x + 3).

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

Done.