Factor completly: f(x)=x^4+x^3−11x^2+x−12

Answer 1

You will use either long division or synthetic division to find the first 1 or 2 terms. It is a trial and error process. In this case, there a just a few options---looking at the last term, we see that the possible factors are 1, 2, 3, 4, and 6. Each one can be + or -

If you have not been taught synthetic division, you can look it up with Google--or just use long division.

To get 12 for the last term, one factor must contain either 3 or 6. I get (x - 3). Dividing this into the original expression, I get:

x^3 + 4x^2 + x + 4

You may be able to see that one of the factors of this must be either (x + 4) or (x + 2)