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

Question

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

Find the possible formula:

Answer 1

P(x) = x²(x - 5)²(x + 1)