x^4-10x^2+9

Question

I have a clue saying that the answer is supposed to be the product of four factors.

The answer keys shows this as the answer...

(x-1)(x+3)(x+1)(x-3)

Although I’m not sure how I would get there.

Answer 1

This is really a quadratic in disguise because if we put y=x² it becomes y²-10y+9=(y-9)(y-1).

Substituting back we get factors x²-9 and x²-1 which both factorise, giving us:

(x-3)(x+3)(x-1)(x+1).