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 .

Question

Find a possible formula for .

P(x) =

Answer 1

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

(x^2 - 6x +9)(x^3+5x^2) =

x^5 -x^4 -21x^3 +45x^2

just change the sign of the each root and add it to x

square it if it's multiplicity 2, then multiply them altogether. x-0 = x, square it and it's x^2