SOLUTION: Factorize the polynomial {{{ f(x) = x^3 - 7x + 6 }}} completely .Thank-you !

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Question 1060004: Factorize the polynomial +f%28x%29+=+x%5E3+-+7x+%2B+6+ completely .Thank-you !
Found 2 solutions by acw1213, ikleyn:
Answer by acw1213(28) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot factor this, are you sure this is what the question was asking?

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
f%28x%29 = x%5E3+-+7x+%2B+6+ = (x-1)*(x-2)*(x+3).

Hint: You can easily check that 1 is the root of the polynomial x%5E3+-+7x+%2B+6+.

Then divide the given polynomial by (x-1) (long division) without a remainder, according to the "Remainder Theorem".

Then analyse the obtained quadratic quotient.
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From Wikipedia (https://en.wikipedia.org/wiki/Polynomial_remainder_theorem): 

     The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial  x-a is equal to  f(a).      

     In particular,  x-a is a divisor of  f(x) if and only if f(a)=0.