Question

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=-5

Answer 1

It means P(x) = (x)(x)(x-3)(x-3)(x+5)

xx(x−3)(x−3)(x+5)
=(xx(x−3)(x−3))(x+5)
=(xx(x−3)(x−3))(x)+(xx(x−3)(x−3))(5)
=x^5−6^x4+9^x3+5x^4−30x^3+45x^2
=x^5−x^4−21x^3+45^x2