How To Find The Function of A Third Degree Polynomial When Given The Zeros of x=-3, x=2, and x=3?

Question

I was given a problem where the question asked me to find which of the answers provided could not be a potential factor in the equation. The information given to figure this out was that the equation was a Third-Degree Polynomial with zeros at -3, 2, and 3. However, I found myself getting stuck, unable to figure out the equation or anything else about the graph. What is the proper way to go about this type of problem and what is the answer to the question given?

Answer 1

You will need to take the three factors of (x + 3), (x - 2) and (x - 3) and multiply them together to get the third degree polynomial specified. I used the box method, then graphed the result. Check the video to see how.

Great problem!

Answer 2

x=-3, x=2, x=3

Let x+3=0, x-2=0, and x-3=0 be algebraic equations created from x=-3, 2, and 3,

let a polynomial f(x)-=(x+3)(x-2)(x-3)

this polynomial is guaranteed to have x=-3, x=2, and x=3 as zeros.