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Suppose that the polynomial function \( f \) is defined as follows. \[ f(x)=3 x^{3}(x-6)^{2}(x+12)(x-11)^{3} \] List each zero of \( f \) according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is zero(s) of multiplicity one: zero(s) of multiplicity two: zero(s) of multiplicity three:

Ask by Vaughn John. in the United States
Feb 25,2025

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Answer

Zero(s) of multiplicity one: -12 Zero(s) of multiplicity two: 6 Zero(s) of multiplicity three: 0, 11

Solution

The zeros and their respective multiplicities are as follows: • Zero(s) of multiplicity one: -12 • Zero(s) of multiplicity two: 6 • Zero(s) of multiplicity three: 0, 11

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The zeros of the polynomial function \( f(x)=3 x^{3}(x-6)^{2}(x+12)(x-11)^{3} \) can be listed according to their multiplicities as follows: zero(s) of multiplicity one: \(-12\) zero(s) of multiplicity two: \(6\) zero(s) of multiplicity three: \(0, 11\)

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