Question

HelloI need some assistance with this question. I provided an answer, but it was incorrect. The images are enclosed.

Answer 1

Given:

There are given that the zeroes and degrees of the polynomial:

$\begin{gathered} \text{zeros:}-2,2,4 \\ \text{Degres:}3 \end{gathered}$

Explanation:

From the concept of a polynomial:

A polynomial has a as zero if and only if (x -a) is a factor of the polynomial.

Then,

From the given polynomial:

$f(x)=(x+2)(x-2)(x-4)$

Then,

$\begin{gathered} f(x)=(x+2)(x-2)(x-4) \\ f(x)=(x^2-2x+2x-4)(x-4) \\ f(x)=(x^2-4)(x-4) \\ f(x)=x^3-4x^2-4x+16 \end{gathered}$

Final answer:

Hence, the polynomial is shown below:

$f(x)=x^3-4x^2-4x+16$