Question

Find the zeros of the polynomial function (show all work) f(x)=x^3 x^2-4x-4

(PLEASE ANSWER ASAP)

Answer 1

The zeros are -2, -1 and 2.

Explanation:

I will assume that it is:

x^3 + x^2 - 4x - 4 = 0

Looks like x = -1 might be a root:

(-1)^3 + (-1)^2 - 4(-1) - 4

= - 1 + 1 + 4 - 4 = 0

So x = -1 is one zero.

As x = -1 is a zero then (x + 1) must be a factor of the expression so we divide:-

x + 1 ( x^3 + x^2 - 4x - 4 ( x^2 - 4 <------- The quotient

x^3 + x^2

-4x - 4

-4x - 4

So we have (x + 1)(x^2 - 4) = 0

(x + 1)(x - 2)(x + 2) = 0

Therefore the zeroes are -1,2 and -2,