How do you find a polynomial function of degree 4 with -2 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1?

1 Answer
Alan P.
Oct 19, 2015

#x^4+6x^3+12x^2+8x#

Explanation:

#y_a=(x+2)(x+2)(x+2) =x^3+6x^2+12x+8#
has #(-2)# as its only root (but with multiplicity of #3#)

#y_b =x#
has #(0)# as its only root (multiplicity of #1#)

#y = y_a* y_b = x^4+6x^3+12x^2+8x#
has #(-2)# as a root (multiplicity #3#) and #(0)# as a root (multiplicity (1))
and is of degree #4#

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