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

$x^{3} - 12 x - 16$ $x^3-12x-16$

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

${(x + 2)}^{2}$ $(x+2)^2$ that is null if x=-2, multiplicity 2,

and

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

${(x + 2)}^{2} (x - 4)$ $(x+2)^2(x-4)$

$(x^{2} + 4 x + 4) (x - 4)$ $(x^2+4x+4)(x-4)$

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

that's

$x^3-12x-16$