Question

Find all of the zeros of the polynomial function:

f(x)=−12x 3 −44x³−40x
A) -4, -2, 0
B) -2, -1, 1
C) -4, -1, 5
D) -1, 2, 4

Answer 1

The zeros of the given polynomial function are 0, -1, and -10.

Step-by-step explanation:

To find the zeros of the polynomial function f(x) = -12x^3 - 44x^2 - 40x, we set the function equal to 0 and solve for x:

-12x^3 - 44x^2 - 40x = 0

Factoring out -4x, we get:

-4x(x^2 + 11x + 10) = 0

Setting each factor equal to 0, we have:

-4x = 0 or x^2 + 11x + 10 = 0

Solving -4x = 0 gives x = 0, and factoring x^2 + 11x + 10 = 0 gives (x + 1)(x + 10) = 0. So x = -1 or x = -10.

Therefore, the zeros of the polynomial function f(x) = -12x^3 - 44x^2 - 40x are x = 0, -1, and -10.