need help with synthetic division?

Question

how do you solve (3x to the 4th - 6x to the 3rd - 2x squared + x - 6) / (x+1) ? i just need help figuring out how to set it up.

Answer 1

(3x^4 - 6x^3 - 2x^2 + x - 6)/(x-1)

Use polynomial long division (see link for longer explanation):

..........3x^3 - 9x^2 + 7x - 6 (solution!)
.......... ______________________
(x - 1)|3x^4 - 6x^3 - 2x^2 + x - 6
.......... 3x^4 - 3x^3
.................. - 9x^3 - 2x^2
.................. - 9x^3 + 9x^2
............................... 7x^2 + x
............................... 7x^2 - 7x
....................................... - 6x - 6

For Synthetic Division, you just use the coefficients to achieve the same thing:

-1 | 3 -6 -2 1 -6
... | -3 9 -7 6
... | 3 -9 7 -6 0 = 3x^3 - 9x^2 + 7x - 6