Question

Using synthetic division, find (2x4 + 4x3 + 2x2 + 8x + 8) ÷ (x + 2).

Answer 1

Answer:

A.) 2x³ + 2x + 4

Step-by-step explanation:

Our divisor is (x+2).  We use -2 in the box and write the coefficients of the dividend:

-2 | 2    4    2    8    8

_____________ __

We drop the 2 from the dividend down:

-2 | 2    4    2    8    8

________________

     2

Multiply the -2 in the box by this 2 and write the answer below the 4 in the dividend.  Add this to the 4 and write the answer below:

-2 | 2    4    2    8    8

           -4                  

     2    0

Multiply the -2 in the box by 0 and write it below the 2 in the dividend.  Add this to the 2 and write the answer below:

-2 | 2    4    2    8    8

           -4   0            

     2    0    2

Multiply the -2 in the box by this 2 and write it below the first 8 in the dividend.  Add this to the 8 and write the answer below:

-2 | 2    4    2    8    8

          -4    0    -4    

      2   0    2    4

Multiply the -2 in the box by this 4 and write it below the last 8 in the dividend.  Add this to the 8 and write the answer below:

-2 | 2    4    2    8    8

          -4    0   -4    -8

      2    0    2    4    0

Since this last digit is 0, this tells us the remainder is 0.

This gives us our answer of 2x³+0x²+2x+4, or 2x³+2x+4.

Answer 2

To do synthetic division take the possible zero of x+2 (the divisor) and get -2, then take this and the coefficients of the polynomial and set up like the picture.