Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Write the equation of this cubic polynomial function.

Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?

-5 is the answer

The linear factors of the cubic are

(x-2)(x-3)(x-5)

To solve for the leading coefficient, use
✔ –5 = a(0 – 2)(0 – 3)(0 – 5)
.
a =
✔ 1/6

Write the function:

f(x) = ⇒ 1/6
x3 =-⇒ 5/3
x2 =-⇒ 31/6
x ⇒ 5