Question

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=4 and x=0, and a root of multiplicity 1 at x=-5 Find a possible formula for P(x) .

Answer 1

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Answer 2

\(
P(x)=(x-2)^2 x^2 (x+5)
\)

Answer 3

\[
P(x)=20 x^2 - 16 x^3 + x^4 + x^5
\]

Answer 4

After expanding

Answer 5

A Mathematica 9 plot is attached.