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=−5

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=-5 

Find a possible formula for p(x)

P(x)=

Answer 1

x^2(x-1)^2(x+5) = x^2(x^2-2x+1)(x+5)=

x^2(x^3-2x^2+x +5x^2-10x+5) =

x^2(x^3+3x^2-9x+5) =

x^5+3x^4-9x^3+5x^2