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f(x) = x³ -6x² -16x. (Simplified)

Step-by-step explanation:

Given:

Zeros: -2, 0, 8; degree: 3

To begin, write the polynomial in factored form involving the zeros:

f(x) = x(x + 2)(x - 8).

If you were to convert this to standard form, you would FOIL the factors:

f(x) = x(x + 2)(x - 8)

f(x) = x(x² -6x -16)

f(x) = x³ -6x² -16x. This is your equation in standard form.