Question

Factorise: $4x^4+7x^2-2$

Answer 1

Let $x^2=p$, then the equation $4x^4+7x^2-2$ becomes $4p^2+7p-2$

Consider the expression $4p^2+7p-2$ and factorise it as follows:

$4p^2+7p-2=4p^2+8p-p-2=4p(p+2)-1(p+2)=(4p-1)(p+2)$

Now, substitute the value of $p$ as $p=x^2$:

$(4p-1)(p+2)=(4x^2-1)(x^2+2)=(2x+1)(2x-1)(x^2+2)$ (Using identity $a^2-b^2=(a+b)(a-b)$)

Hence, $4x^4+7x^2-2=(2x+1)(2x-1)(x^2+2)$