Question

Which of the following is the correct factorization of the polynomial below?

x3 + 12x2 + 36x

Answer 1

D is the answer. x(x^2+12x+36)
= x(x+6)^2

Answer 2

Answer:

Option (d) is correct.

The correct factorization of the polynomial $x^3+12x^2+36x$ is $x(x+6)^2$

Step-by-step explanation:

Given : Polynomial  $x^3+12x^2+36x$

We have to factorize the given polynomial  $x^3+12x^2+36x$.

Consider the given equation  $x^3+12x^2+36x$

Taking x common from each term, we have,

$x^3+12x^2+36x=x(x^2+12x+36)$

Rewrite 36 as $6^2$ , we get,

$x(x^2+12x+36)=x(x^2+12x+6^2)$

Using Algebraic identity, $\left(a+b\right)^2=a^2+2ab+b^2$

We have,

$a=x,\:b=6$

$x(x^2+12x+6^2)=x(x+6)^2$

Thus, The correct factorization of the polynomial $x^3+12x^2+36x$ is $x(x+6)^2$