SOLUTION: Can someone help me please? The polynomial function r(x) at right is of at least possible degree and has zeroes at -4,-2,0 and 2, and also passes through the point (-1,3). Find th

Question 1090850: Can someone help me please?
The polynomial function r(x) at right is of at least possible degree and has zeroes at -4,-2,0 and 2, and also passes through the point (-1,3). Find the equation for r(x) in factored form.(I could not draw the graph here...)
Thank you.

Answer by greenestamps(13367) (Show Source): You can put this solution on YOUR website!

A polynomial with four zeros has degree 4 or greater. Since you are looking for the polynomial of least possible degree that has the four give zeros, you want a polynomial of degree exactly 4. Since it has zeros -4, -2, 0, and 2, it will be of the form

The constant a will determine how "steep" or "flat" the graph of the function is. In particular, it will determine the exact value of the function for any given x value.

So substitute the given x value, -1, into the polynomial and determine the value of a that will produce the given y value, 3:

When you have finished solving that equation to determine the value of a, you can write the complete polynomial function.

In response to your message...

Yes, a is 1/3; and yes, that is factored form. So the polynomial is

When I graph that polynomial on my graphing calculator, it has zeros at -4, -2, 0, and 2; and it passes through (-1,3).

Do you have a picture of what the graph is supposed to look like and it looks different?