College Algebra Polynomial Functions

Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 1 at x=−3. The y-intercept is y=−45.

Find a formula for P(x).

Answer 1

P(x) = C(x-5)^2 (x+3)

P(0) = -45

-45 = C(-5)^2(3)

-45 = C(25)(3)

-45 = 75C

C = -45/75 = -3/5

P(x) = (-3/5)(x-5)^2(x+3)