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=-3, how do you find a possible formula for P(x)?
Each root corresponds to a linear factor, so we can write:
#P(x) = x^2(x-1)^2(x+3)#
Any polynomial with these zeros and at least these multiplicities will be a multiple (scalar or polynomial) of this
Strictly speaking, a value of