Question

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

Answer 1

First Option is correct.

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

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)