Question

The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−3.
Find a possible formula for P(x). P(x)=,

Answer 1

Sine the roots x=1 and x=0 have a multiplicity of 2, we know p(x)= (x-1)^2 (x)^2 (x-a). Since we also know x=-3 is a root, we have p(x)= (x-1)^2 x^2 (x+3)