SOLUTION: I was told to find all roots of the polynomial x^3-x^2+16x-16. Is it 1,4,-4? -1,4,-4? or do I add an "i" in any of them?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I was told to find all roots of the polynomial x^3-x^2+16x-16. Is it 1,4,-4? -1,4,-4? or do I add an "i" in any of them?      Log On


   

Question 65545: I was told to find all roots of the polynomial x^3-x^2+16x-16.
Is it 1,4,-4? -1,4,-4? or do I add an "i" in any of them?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I was told to find all roots of the polynomial x^3-x^2+16x-16.
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The coefficients add up to zero, so x=1 is a root.
Then using synthetic division you find:
1)....1....-1....16....-16
.......1.....0.....16.| 0
Quotient: x^2+16
Remainder: 0
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Now you knowf(x)=(x-1)(x^2+16)
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But x^2+16 = (x+4i)(x-4i)
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So the final answer is
f(x)=(x-1)(x-4i)(x+4i)
Cheers,
Stan H.