Question

Find a polynomial function of degree 7 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 1 as a zero

Answer 1

The polynomial function is P(x) = x^3(x + 1)^3(x -1)

How to determine the polynomial function?

The zeros of the polynomial and the multiplicities are given as:

• -1 as a zero of multiplicity 3,
• 0 as a zero of multiplicity 3,
• 1 as a zero of multiplicity 1

The degree is given as

Degree = 7

The polynomial is represented as:

P(x) = (x - zero)^multiplicity

Using the above format, we have

P(x) = (x + 1)^3(x - 0)^3(x -1)

This gives

P(x) = x^3(x + 1)^3(x -1)

Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)

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