Factorise the following polynomial: $x^3 + x^2- 4x - 4$.

Given :

The given polynomial is  $x^3 + x^2- 4x - 4$.

To do:

We have to factorize the given polynomial.

Solution :

We know that,

$a^2-b^2= (a+b)(a-b)$

$x^3+x^2-4x-4 = x^2 (x+1)-4(x+1)$

                       $= (x^2-4)(x+1)$

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

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

Therefore,

The factors of the polynomial$x^3 + x^2- 4x - 4$ are $(x+1),(x+2)$ and $(x-2)$.

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Updated on: 10-Oct-2022

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