Question

Find the factors of f(x), given that x = −2 is a zero. HELP PLEASE!!

Answer 1

Answer:

First Option is correct.

(x+2)(x+3)(x-4)

Step-by-step explanation:

Given:

The given factor is.

$f(x)=x^{3}+x^{2}-14x-24$

We need to find the factors of given factor.

Solution:

$f(x)=x^{3}+x^{2}-14x-24$

Substitute (-4x-10x) in the place of -14x

$f(x)=x^{3}+x^{2}-4x-10x-24$

Rearrange the equation:

$f(x)=(x^{3}-4x)+(x^{2}-10x-24)$

Now we factorised the above equation.

The factors of $x^{2} -10x-24=(x+2)(x-12)$

Now we substitute (x+2)(x-12) in the place of $x^{2} -10x-24$

And in the place of $x^{3}-4x=x(x^{2}-4)$

$f(x)=x(x^{2}-4)+(x+2)(x-12)$

Simplify $x^{2} -4=x^{2} -(2)^{2} = (x+2)(x-2)$

$f(x)=x[(x+2)(x-2)]+(x+2)(x-12)$

Common factor for above function (x+2)

$f(x)=(x+2)[x(x-2)+(x-12)]$

Simplify.

$f(x)=(x+2)[x^{2}-2x+x-12]$

$f(x)=(x+2)(x^{2}-x-12)$

The factor of $x^{2}-x-12=x^{2}-4x+3x-12=x(x-4)+3(x-4)=(x-4)(x+3)$

So the factors of the function.

$f(x)=(x+2)(x-4)(x+3)$

Therefore, the factors of the given function are (x+2)(x-4)(x+3)