SOLUTION: Write a polynomial function in standard form with the given zeros. x= 1,-1, -2

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Question 716099: Write a polynomial function in standard form with the given zeros.
x= 1,-1, -2

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A polynomial function with zeros z%5B1%5D, z%5B2%5D, z%5B3%5D, etc. will have a factored form of:
f%28x%29+=+a%28x+-+z%5B1%5D%29%28x+-+z%5B2%5D%29%28x+-+z%5B3%5D%29...
where "a" is any non-zero number.

For a polynomial with the given zeros, its factored form will be:
f%28x%29+=+a%28x-1%29%28x-%28-1%29%29%28x-%28-2%29%29
Since we can pick any non-zero number for "a", there will be a different f(x) for every possible "a". So there is not just one function with the given zeros. To find one such function we will pick a value for "a". To make things easy, we'll make "a" be 1:
f%28x%29+=+%28x-1%29%28x-%28-1%29%29%28x-%28-2%29%29
All we have left to do is put the equation into the requested standard form. So we simplify:
f%28x%29+=+%28x-1%29%28x%2B1%29%28x%2B2%29
We can use the %28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2 pattern to quickly multiply the first two factors:
f%28x%29+=+%28x%5E2-1%29%28x%2B2%29
Now we use FOIL to multiply the remaining factors:
f%28x%29+=+x%5E2%2Ax%2Bx%5E2%2A2%2B%28-1%29%2Ax%2B%28-1%29%2A2
Continuing the simplifying...
f%28x%29+=+x%5E3%2B2x%5E2%2B%28-x%29%2B%28-2%29
This is a polynomial function, in standard form, with the given zeros.