SOLUTION: find a polynomial f(x) of degree 3 that satisfies the following condition: -2 is a zero of multiplicity 3; f(-1) = 4

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Question 241535: find a polynomial f(x) of degree 3 that satisfies the following condition: -2 is a zero of multiplicity 3; f(-1) = 4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
With -2 a zero of multiplicity 3, f(x) will be of the form q%28x+-+%28-2%29%29%5E3 or q%28x+%2B+2%29%5E3 where q is some constant. And we can use f(-1) to find q:
4+=+q%28%28-1%29+%2B+2%29%5E3
4+=+q%281%29%5E3
4+=+q
So f%28x%29+=+4%28x%2B2%29%5E3. Since we are asked to find f(x) as a polynomial, we will need to multiply this out:
f%28x%29+=+4%28x%2B2%29%5E3
f%28x%29+=+4%28x%2B2%29%5E2%28x%2B2%29
Since %28x%2B2%29%5E2+=+x%5E2+%2B+4x+%2B+4:
f%28x%29+=+4%28x%5E2+%2B+4x+%2B+4%29%28x%2B2%29
f%28x%29+=+4%28x%5E3+%2B+2x%5E2+%2B4x%5E2+%2B8x+%2B+4x+%2B+8%29
f%28x%29+=+4%28x%5E3+%2B6x%5E2+%2B+12x+%2B+8%29
f%28x%29+=+4x%5E3+%2B+24x%5E2+%2B48x+%2B+32