Question 824421: Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1
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Since the sum of the coefficients is zero, x = 1 is a root
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Use synthetic division to find other roots.
1)....3....-6....4....-2....1
......3....-3....1....-1..|..0
Again; since the sum of the coefficients is 1, x = 1 is a root
1)....3....-3....1....-1
......3....0.....1...|..0
Quotient: 3x^2+1 = 0
Factor::
(sqrt(3)x+i)(sqrt(3)x-i) = 0
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Roots:: x = 1,1,sqrt(3)i/3,-sqrt(3)i/3
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Factor Form
f(x) = (x-1)^2(3x^2+1)
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Cheers,
Stan H.
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