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 Answered2023-01-01

Answer & Explanation

halliekorinnbsn Expert2023-01-02Added 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:

\underset{―}{f (x) = x {(x + 4)}^{3}}

Or, in expanded form, is

\underset{―}{f (x) = x^{4} + 12 x^{3} + 48 x^{2} + 64 x}

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