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

Deacon Hensley

Deacon Hensley

Answered question

2023-01-01

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

Answer & Explanation

halliekorinnbsn

halliekorinnbsn

Beginner2023-01-02Added 13 answers

We're given that there are zeros at x=4 (mult. 3) and at x=0 (mult. 1).
Since the zero at x=4 has multiplicity three, we can write it as the factor (x+4) raised to the third power:
f(x)=(x+4)3
Additionally, x=0 has a zero, so we can add an x:
f(x)=x(x+4)3
Or, in expanded form, is
f(x)=x4+12x3+48x2+64x

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