Question

Factorise the following: $x^4-5x^2+4$

Answer 1

Given that: $x^4-5x^2+4$

$=x^4-4x^2-x^2+4$, (split the middle term)

$=(x^4-4x^2)+(-x^2+4)$, (group pair of terms)

$=x^2(x^2-4)-1(x^2-4)$, (factor each binomials)

$=(x^2-4)(x^2-1)$, (factor out common factor $(x^2-4)$)

$=(x^2-2^2)(x^2-1^2)$

$=(x+2)(x-2)(x+1)(x-1)$, (since $x^2-b^2=(x+b)(a-b)$)