Question

What are the zeros of the polynomial function f(x) = x^3 + 2x^2 − 24x?

a. −6, 0, 4
b. 6, 0, −4
c. −6, 0, −4
d. 6, 0, 4

Answer 1

The zeros of the polynomial function f(x) = x^3 + 2x^2 − 24x are found by factoring out x and factoring the resulting quadratic equation to get x(x + 6)(x - 4). Setting each factor equal to zero gives us the zeros −6, 0, 4.

Step-by-step explanation:

The zeros of a polynomial function are the values of x that make the function equal to zero. For the polynomial f(x) = x^3 + 2x^2 − 24x, we can find the zeros by first factoring out the greatest common factor, which in this case is x:

f(x) = x(x^2 + 2x − 24).

Next, we factor the quadratic equation x^2 + 2x - 24 which factors into (x + 6)(x - 4). So, our factored polynomial is now:

f(x) = x(x + 6)(x - 4).

Setting each factor equal to zero, we get the zeros:

• x = 0
• x = -6
• x = 4

Therefore, the zeros of the polynomial function are −6, 0, 4.