SOLUTION: I have to write a polynomial Function using these roots -1,-1,1 How do I do this??

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Question 711966: I have to write a polynomial Function using these roots
-1,-1,1
How do I do this??
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In general, a polynomial that has r as a root will have a factor of (x-r). So the polynomial we are looking for will have factors of:
P%28x%29+=+%28x-%28-1%29%29%28x-%28-1%29%29%28x-1%29
which simplifies to:
P%28x%29+=+%28x%2B1%29%28x%2B1%29%28x-1%29

Now all we have to is multiply this out. We can take advantage of the %28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2 pattern to multiply the first two factors. Or we can take advantage of the %28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2 pattern to multiply the last two factors. (Remember, with multiplication the order does not matter!) Since the second pattern has a simpler result I'm going to use it to multiply the last two factors:
P%28x%29+=+%28x%2B1%29%28%28x%29%5E2-%281%29%5E2%29
which simplifies to:
P%28x%29+=+%28x%2B1%29%28x%5E2-1%29
Now we multiply the remaining factors. They do not fit any pattern so we must resort to FOIL:
P%28x%29+=+x%2Ax%5E2-x%2A1%2B1%2Ax%5E2-1%2A1
which simplifies...
P%28x%29+=+x%5E3-x%2Bx%5E2-1
Rearranging the terms so they are in standard form:
P%28x%29+=+x%5E3%2Bx%5E2-x-1

P.S. When I described the factored form of a polynomial, I left out a minor detail. The general factored form of a polynomial is:
P(x) = a * (x-r) ... (with as many (x-r) factors as there are roots).
The "a" can be any non-zero number and it is the part I left out. The answer we got while ignoring the "a" has, in effect, an "a" of 1. Fell free to re-do the solution and pick a different "a".