Question

What are the zeros of the polynomial function f(x) = x3 − x2 − 12x?

Answer 1

X^3-x^2-12x=0  factor out x

x(x^2-x-12)=0  factor parenthetical expression

x(x^2-4x+3x-12)=0

x(x(x-4)+3(x-4))=0

x(x+3)(x-4)=0

So x=-3, 0, 4

So c) 0, 4, -3

Answer 2

Answer:

The correct option is c.

Step-by-step explanation:

The given function is

$f(x)=x^3-x^2-12x$

Taking out the common factors.

$f(x)=x(x^2-x-12)$

Now, factorize the parenthesis.

$f(x)=x(x^2-4x+3x-12)$

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

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

Equate the function equal to 0, to find the zeros of the polynomial function f(x).

$f(x)=0$

$x(x-4)(x+3)=0$

Using zero product property, we get

$x=0$

$x-4=0\Rightarrow x=4$

$x+3=0\Rightarrow x=-3$

The zeros of the polynomial function f(x) are 0,4,-3. Therefore the correct option is c.