How do you form a polynomial function whose zeros, multiplicities and degrees are given: Zeros: -2, multiplicity 2; 4, multiplicity 1; degree 3?

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Answer 1 · 2016-07-01T09:55:27

#x^3-12x-16#

the polynomial will be composed by the product of 3 (due to the degree) bynomials with degree 1:

#(x+2)^2# that is null if x=-2, multiplicity 2,

and

x-4 that is null if x=4, so the polynomial is obtained by multiplyng:

#(x+2)^2(x-4)#

#(x^2+4x+4)(x-4)#

#x^3cancel(-4x^2)cancel(+4x^2)-16x+4x-16#

that's

#x^3-12x-16#