SOLUTION: Please explain the steps to finding the GCF of the following: (I have provided the answer, but do not understand the process to get the correct answer.) (x-1)^3+4(x-1)^2+3(x-1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please explain the steps to finding the GCF of the following: (I have provided the answer, but do not understand the process to get the correct answer.) (x-1)^3+4(x-1)^2+3(x-1)       Log On


   

Question 69659: Please explain the steps to finding the GCF of the following: (I have provided the answer, but do not understand the process to get the correct answer.)
(x-1)^3+4(x-1)^2+3(x-1)
Answer:x(x-1)(x+2)
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-1%29%5E3%2B4%28x-1%29%5E2%2B3%28x-1%29%29
%28%28x-1%29%5E3%2F%28x-1%29%2B4%28x-1%29%5E2%2F%28x-1%29%2B3%28x-1%29%2F%28x-1%29%29 [Look for a common factor. Divide each term by the common factor (x-1)]
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%28%28x-1%29%28x-1%29%5E2%2B4%28x-1%29%2B3%29 [Cancel-out wherever possible and factor out-the common factor]
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%28%28x-1%29%28x-1%29%28x-1%29%2B4x-4%2B3%29[Simplify wherever possible. Look for any more common factors. If none, try to simplify.
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%28+%28x-1%29%28x%5E2-2x%2B1%2B4x-4%2B3%29%29
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%28+%28x-1%29%28x%5E2%2B2x%29%29
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%28%28x-1%29%28x%5E2%2Fx%2B2x%2Fx%29+%29[Try to factor-out any common factors, if possible. The common factor is "x", so divide each term by "x"].
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%28%28x-1%29%28x%29%28x%2B2%29%29[Cancel wherever possible. Try to factor again. If unable to factor or simplify any further, the problem is complete.