Find formula for P(x)

Question

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,128).
Find a formula for P(x).
P(x)=

Answer 1

P(x) = A(x-1)²(x)(x+3)

 

128 = P(5) = A(5-1)²(5)(5+3) = A(16)(5)(8) = A(640)

 

A = 128/640 = 0.2 = 1/5

 

P(x) = (1/5)(x-1)²(x)(x+3)