What are the zeros of the polynomial function f(x) = x3 − 2x2 − 24x?

x = 0, x = -4, and x = 6

Step-by-step explanation:

To find the zeros of this polynomial, we can begin by factoring out a common factor of each term. 'x' is a common factor. We can distribute this variable out, giving us:

f(x) = x(x²- 2x- 24)

Now, factor the polynomial inside of the parenthesis into its simplest form. Factors of -24 that add up to -2 are -4 and 6.

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

From this, we can derive the zeros x = 0, x = -4 and x = 6.

step-by-step explanation:

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