SOLUTION: I need help with this problem Construct a polynomial function with the stated properties Third degree, only real coefficients, -4 and 4+4i are two of the zeros, y-intercept is -6

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Question 369473: I need help with this problem
Construct a polynomial function with the stated properties
Third degree, only real coefficients, -4 and 4+4i are two of the zeros, y-intercept is -68
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since x=4%2B4i is a root, then so is x=4-4i since complex roots only come in complex conjugate pairs.
f%28x%29=a%28x%2B4%29%28x-%284%2B4i%29%29%28x-%284-4i%29%29
f%28x%29=a%28x%2B4%29%28x%5E2-8x%2B32%29
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.
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f%280%29=a%284%29%2832%29=-68
a%28128%29=-68
a=-%2868%2F128%29=-17%2F32
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highlight%28f%28x%29=-%2817%2F32%29%28x%2B4%29%28x%5E2-8x%2B32%29%29