SOLUTION: Factor the polynomial p(x) = 2x^3-9x^2+7x+6 given the fact that x=2 is a root of the polynomial.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the polynomial p(x) = 2x^3-9x^2+7x+6 given the fact that x=2 is a root of the polynomial.      Log On


   

Question 630658: Factor the polynomial p(x) = 2x^3-9x^2+7x+6 given the fact that x=2 is a root of the polynomial.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If x=2 is a root, then (x-2) is a factor. To find the other factor(s) we divide p(x) by (x-2). This is most easily done with synthetic division. (If you don't know synthetic division then use long division.)

2 |   2   -9    7   6
===        4  -10   6
     ================
      2   -5   -3   0

The remainder (in the lower right corner) in zero which means that (x-2) divided evenly. (We should have expected this since factors of something will divide evenly into it.) The rest of the bottom row tells us the other factor. "2 -5 -3" translates into 2x%5E2-5x-3. So
p%28x%29+=+%28x-2%29%282x%5E2-5x-3%29
We can now use factoring techniques (trinomial factoring) to factor the second factor further:
p%28x%29+=+%28x-2%29%282x%2B1%29%28x-3%29
p(x) is now fully factored.