Math Help Find a formula of P(x)

Question

The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=1x=1 and a root of multiplicity 11 at x=−5x=-5. The yy-intercept is y=−3y=-3.

Find a formula for P(x)P(x).

Answer 1

P(x) = a(x-1)^22(x+5)^11

P(0)=-3=a(-1)^22(5)^11= a(5)^11

a=-3/(5)^11

P(x)= (-3/5^11)(x-1)^22(x+5)^11