The function f(x) is a cubic function and the zeros of f(x) are -6, -3 and 1. The y-intercept of f(x) is 90. Write the equation of the cubic polynomial in standard
form.

Step-by-step explanation:

Equation of a Polynomial

Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:

Where a is the leading coefficient.

We know the three roots of the polynomial -6, -3, and 1, thus:

Since the y-intercept of the polynomial is y=90 when x=0:

90=a(0+6)(0+3)(0-1)

90=a(6)(3)(-1)=-18a

Thus

a = 90/(-18) = -5

The polynomial is:

We must write it in standard form, so we have to multiply all of the factors as follows:

        532.60

        x   8.53

          159780

+      2663000

     42608000

      4543.0780