Question

Factor completely. x 3 + 6x 2 - 4x - 24

Answer 1

I really suck at explaining with words so here a photo, I hope you understand
A

Answer 2

Answer:

Option (a) is correct.

The factored form of given expression $x^3+6x^2-4x-24$ is $(x+6)(x+2)(x-2)$

Step-by-step explanation:

  Given  expression $x^3+6x^2-4x-24$

We have to factorize the given expression completely.

Consider the given expression $x^3+6x^2-4x-24$

We will solve the given expression by grouping terms and taking common factor common.

$x^3+6x^2-4x-24$

Taking $x^2$ common from first two terms and  -4 common from last two terms, we have,

$x^2(x+6)-4(x+6)$

Taking (x+6) common , we have,

$x^2(x+6)-4(x+6)=(x+6)(x^2-4)$

Also , using algebraic identity $a^2-b^2=(a+b)(a-b)$

We have a = x , b = 2

We have,

$x^2(x+6)-4(x+6)=(x+6)(x^2-4)$

$\Rightarrow (x+6)(x^2-4)=(x+6)(x+2)(x-2)$

Thus, the factored form of given expression $x^3+6x^2-4x-24$ is $(x+6)(x+2)(x-2)$