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

Question

The y -intercept is y = − 15 . Find a formula for P ( x ) .

Answer 1

p(x) = a(x - 5)²(x + 2)

Since p(0) = -15, 50a = -15. So, a = -3/10.

Therefore, p(x) = -(3/10)(x - 5)²(x + 2)

Answer 2

P(x) = (x - 5)²(x + 2)