The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 5 and a root of multiplicity 1 at x = − 5. The y -intercept is y = - 75 . Find a formula for P ( x ) .

Answer 1

p(x) = A(x - 5)²(x + 5)

p(0) = -75

-75 = A(-5)²(5) = 125A

A = -75/125 = -3/5

p(x) = (-3/5)(x - 5)²(x + 5)