We want to find the zeros of this polynomial:

p (x) = 3x^3 - 3x^2 - 18x

x=0 x=3 x=-2

Step-by-step explanation:

p (x) = 3x^3 - 3x^2 - 18x

Factor out the greatest common factor, 3x

p (x) = 3x (x^2 - x - 6)

Factor inside the parentheses

What 2 numbers multiplies to - 6 and adds to - 1

-3*2 = - 6

-3+2 = - 1

p (x) = 3x (x-3) (x+2)

Setting the function equal to zero to find the zeros

0 = 3x (x-3) (x+2)

Using the zero product property

3x = 0 x-3 = 0 x+2 = 0

x=0 x=3 x=-2

x = - 2, 0, 3.

Step-by-step explanation:

3x^3 - 3x^2 - 18x = 0

First take out the GCF which is 3x:

3x (x^2 - x - 6) = 0

So one zero is 0 (because 3x = 0).

x^2 - x - 6 = 0

(x - 3) (x + 2) = 0

x = - 2, 3.