Question 611141: Factor over complex numbers
4X^4-4X^3+5X^2-4X+1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Factor over complex numbers
4X^4-4X^3+5X^2-4X+1
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I graphed it and found a zero at 1/2
Use sythetic division:
1/2)....4....-4....5....-4.....1
.........4....-2....4.....-2...|..0
Quotient: 4x^3 -2x^2 + 4x -2 also has a zero at x = 1/2
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(1/2)....4...-2....4....-2
..........4....0...4....|..0
Quotient: 4x^2 + 4
Factor to get:
4(x^2+1) = 0
4(x+i)(x-i) = 0
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Final answer:
Zeroes at x = 1/2 with multiplicity 2
x = i and x = -i
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Cheers,
Stan H.
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