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)?

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##P(x) = x^5+x^4-5x^3+3x^2##

Each parent corresponds to a direct factor, so we can write:

##P(x) = x^2(x-1)^2(x+3)##

##=x^2(x^2-2x+1)(x+3)##

##= x^5+x^4-5x^3+3x^2##

Any polynomial delay these nothings and at last these multiplicities conquer be a multiple (scalar or polynomial) of this ##P(x)##

Footnote

Strictly weighty, a prize of ##x## that results in ##P(x) = 0## is designated a parent of ##P(x) = 0## or a nothing of ##P(x)##. So the inquiry should unquestionably enjoy vocal about the nothings of ##P(x)## or about the parents of ##P(x) = 0##.

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