Question

Which of the following polynomials below is identical to the polynomial $(x^2-1)(x^2-4)$?

• A. $x^4+4$
• B. $x^2+5x+4$
• C. $(x^2+1)(x^2+4)$
• D. $(x^2+x-2)(x^2-x-2)$

Answer 1

The correct option is D $(x^2+x-2)(x^2-x-2)$

$(x^2-1)(x^2-4)=(x^2-1^2)(x^2-2^2)$
= $(x+1)(x–1)(x–2)(x–2)$
And $(x^2+x-2)(x^2-x-2)$
$=(x^2+2x-x-2)(x^2-2x+x-2)$
= $\left(x\right(x+2)-1(x+2\left)\right)\left(x\right(x–2)+1(x–2\left)\right)$
= $(x–1)(x+2)(x+1)(x–2)$