Chapter 4.1, Problem 108AYU

To determine

To construct: A polynomial function $f$ with the given characteristics.

Answer to Problem 108AYU

$f\left(x\right)=x^3+3x^2-6x+16$

Explanation of Solution

Given:

Zeros $=-4,-1,2$.

Degree $\text{= 3}$.

$Y\text{-intercept}=16$.

The polynomial function $f=\left(x+4\right)\left(x+1\right)\left(x-2\right)+24=x^3+3x^2-6x-8+24$.

$f\left(x\right)=x^3+3x^2-6x+16$