Synthetic Division?

Question

 -2x4 - 6x2 + 3x + 1 divided by x + 1

 

Remainder:      

Remainder Theorem:

Answer 1

You divide by the number being subtracted from x. In x + 1, -1 is being subtracted from x. Then, you use the coefficients of the variables, replacing a missing variable with a zero. So, the problem looks like the following:

-1l -2  0  -6  3  1    First, you bring down the -2.

                         

     -2

 

-1l -2   0   -6   3     1   Now you multiply -1(-2) and add. Repeat.

           2   -2   8   -11      

     -2  2   -8   11  -10

 

These are the coefficients of your answer, including the remainder.  Since you started with x⁴, your answer begins with x³. 

 

Answer: -2x³ + 2x² - 8x +11 -   10   

                                                 x + 1