SOLUTION: Find a third degree polynomial function f(x) with real coefficients that has -3,-2,and 2 as zeros such that f(1)=-12

Question 812405: Find a third degree polynomial function f(x) with real coefficients that has -3,-2,and 2 as zeros such that f(1)=-12
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
A general formula for a 3rd degree polynomial in factored form would be:

where the z's are zeros of the polynomial and the "a" is a non-zero constant. Using the given zeros we get:

which simplifies to:

Now we must multiply this out and find the right value for "a", either one first. First I will find the "a". For this we will use the fact that f(1) = -12:

Simplifying...

Dividing by -12:

So:

Now we multiply this out. I'll start by using the pattern to multiply the last two factors:

which simplifies to:

Using FOIL on what's left:

Reordering into standard form:

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