Question

Tatiana was asked to construct a polynomial function with the following zeros and multiplicities. Which function should she write? Zero Multiplicity x=1 3 x=81 5(1 point) Responses f(x)=(x+1)5(x+81)3 f left parenthesis x right parenthesis equals left parenthesis x plus 1

Answer 1

To construct a polynomial function based on the given zeros and their multiplicities, we need to follow a specific rule. For each zero \(x = a\) with multiplicity \(m\), the corresponding factor in the polynomial is \((x - a)^m\).

Given the zeros and their multiplicities:

- Zero \(x = 1\) with multiplicity \(3\) contributes the factor \((x - 1)^3\).
- Zero \(x = 81\) with multiplicity \(5\) contributes the factor \((x - 81)^5\).

Thus, the polynomial function \(f(x)\) can be written as follows:

\[
f(x) = (x - 1)^3 (x - 81)^5
\]

This is the correct polynomial function Tatiana should write.