Question

Does anyone know how to do synthetic division? I'm so lost.

Answer 1

For (polynomial)/(x-constant)
do

constant | coefients of polynomial
               |___________________

if write 1 for every power, if a power is missing, write 0 tehre
this is kind of complicated
so what you do is start at the top, at the first number inside that wierd thing
bring it down below the line
multiply the left number
move it up and right 1 collumn
add that collumn,  and write the sum below the line
repeat

so for  yours
(x-4) so the constant outside is 4

so
4|1  13  -64  -20  16
  |_______________

bring down the first row thing
4|1  13  -64  -20  16
  |_______________
   1

multily by 4 and move up and right
4|1  13  -64  -20  16
  |___4__________
   1

add
4|1  13  -64  -20  16
  |___4__________
   1    17

multiply and move
4|1  13  -64  -20  16
  |___4__68______
   1    17

add
4|1  13  -64  -20  16
  |___4__68______
   1    17  4

multiply and move
4|1  13  -64  -20  16
  |___4__68_16___
   1    17  4   

add
4|1  13  -64  -20  16
  |___4__68_16___
   1    17  4     -4

multiply and movie
4|1  13  -64  -20  16
  |___4__68_16_-16
   1    17  4     -4

add
4|1  13  -64  -20  16
  |___4__68_16_-16
   1    17  4     -4   0

so the coefients 1,17,4,-4,0
and since we started with 4th degree (x^4) we minus 1 (to get x^3)
1x^3+17x^2+4x-4 and 0 remainder
2nd option is your answer