SOLUTION: How do you solve for polynomial division and factors Q: Divide to determine whether x+1 and x - 3 are factors of x^(3)+2x^(2)-5x-6

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Question 377533: How do you solve for polynomial division and factors
Q: Divide to determine whether x+1 and x - 3 are factors of
x^(3)+2x^(2)-5x-6
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

         x^2 + x - 6
        __________________________
 x + 1 | x^3 +  2x^2 -  5x - 6
      - (x^3 +   x^2)
       ---------------
                 x^2 -  5x  
             -  (x^2 +   x)
                --------------
                       -6x - 6 
                   -  (-6x - 6) 
                      ---------
                             0

+%28x%5E3%2B2x%5E2-5x-6%29%2F%28x%2B1%29+=%28x%5E2%2Bx-6%29
Since the remainder is zero, %28x%2B1%29 is a factor.
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         x^2 + 5x + 10
        __________________________
 x - 3 | x^3 +  2x^2 -  5x -  6
      - (x^3 -  3x^2)
       ---------------
                5x^2 -  5x  
             - (5x^2 - 15x)
                ---------------
                       10x -  6 
                   -  (10x - 30) 
                      ----------
                             24

+%28x%5E3%2B2x%5E2-5x-6%29%2F%28x-3%29+=%28x%5E2%2B5x%2B10%29%2B24%2F%28x-3%29
Since the remainder is not zero, %28x-3%29 is not a factor.
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