SOLUTION: Use the factor theorem so show that x - a is a factor of:
x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .
I would appreciate it if you could help me with the steps.
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: Use the factor theorem so show that x - a is a factor of:
x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .
I would appreciate it if you could help me with the steps.
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Question 635576: Use the factor theorem so show that x - a is a factor of:
x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .
I would appreciate it if you could help me with the steps. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Use the factor theorem to show that x - a is a factor of:
x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .
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Factor Theorem:: x-a is a factor iff f(a) = 0.
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f(x) = x^2(a-b)^3 + a^2(b-x) + b^2(x-a)
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f(a) = a^2(a-b)^3 + a^2(b-a) + b^2(a-a)
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= a^2(a-b)^3 - a^2(a-b) + 0
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= a^2(a-b)[(a-b)^2-1]
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That result does not satisfy the Factor Theorem requirement.
x-a is NOT a factor of f(x)
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Cheers,
Stan H.
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