<PRE><B>Question 319327</B>
Given that -1 is a zero of the polynomial g(x)=x^3-3x^2-3x+1, express g(x) as a product of linear factors.
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If -1 is a zero, use synthetic division to find the other factors:
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-1)....1....-3....-3....1
.......1....-4....1....|..0
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The quadratic factor is x^2-4x+1
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Use the quadratic formula to find the zeroes:
x = [4 +- sqrt(16-4*1)]/2
x = [4 +- sqrt(12)]/2
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x = [4 +- 2sqrt(3)]/2
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x = [2 +- sqrt(3)]
x = 2+sqrt(3) or x = 2-sqrt(3) or x = -1
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Cheers,
Stan H.
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