Question

The function f(x) is a cubic function and the zeros of f(x) are -3, -2, and 1. The y-intercept of f(x) is -24. Write the equation of the cubic polynomial in standard form.

Answer 1

f(x) = 4x³+16x²+4x-24

Explanation:

Factors are (x+3)(x+2)(x-1)

(x+3)(x²+2x-x-2)

(x+3)(x²+x-2)

x³+x²-2x+3x²+3x-6

x³+4x²+x-6

This could have been the function but the intetcept is 6 here.

So we'll take a miltiple of this one such that the intercept becomes-24

-24/-6 = 4

That multiple is 4

f(x) = 4(x³+4x²+x-6)

f(x) = 4x³+16x²+4x-24