SOLUTION: Factor x^3+2x^2-5x-6 given that x+3 ia a factor.

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Question 384334: Factor x^3+2x^2-5x-6 given that x+3 ia a factor.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3%2B2x%5E2-5x-6
If x+3 is a factor then it will divide evenly into x%5E3%2B2x%5E2-5x-6. So we can find the other factor by dividing x%5E3%2B2x%5E2-5x-6 by x+3. We can use long division or synthetic division. I find synthetic division easier. But synthetic division works for divisors in the form x-c where c is some number. So to use synthetic division with x+3 we have to look at it as a subtraction: x - (-3):
-3 |  1   2   -5   -6
----     -3    3    6
      ---------------
      1  -1   -2    0

The zero in the lower right corner is the remainder and a zero remainder means it (x - (-3)) divided evenly (as we were told it would). The rest of the bottom line tells us the quotient (which is the other factor). The 1 -1 -2 translates into x%5E2-x-2

x%5E2-x-2 factors fairly easily into (x-2)(x+1). So
x%5E3%2B2x%5E2-5x-6+=+%28x%2B3%29%28x-2%29%28x%2B1%29