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=-2

Answer 1

What you need to remember is that if a is a root for a polynomial, then (x-a) is a factor of the polynomial. The degree determines whether it is a linear factor or squared or cubed. This polynomial has two roots as double roots so the factors are squared, and the other one is just a linear factor. Multiplying the factors will give you the polynomial since the leading coefficient is 1.

Answer 2

P(x) = (x - 5)²x²(x + 2)