How do I use synthetic division to find the quotient and the remainder of a problem that has exponents in the equation?

Let us have to divide (2x³-4x²+x-5) by (x-2) using synthetic division. 

Then we will consider the coefficients of (2x³-4x²+x-5) , which are 2 , - 4 , 1 , -5 

For x-2 , we set it equal to 0 , so we get x-2=0 or x=2

We will divide by this x=2

The first-term goes down as it is, then we multiply it by the 2, and the result goes below -4. Then add them.

Then again multiply the result by 2 and that goes below 1. Then again add and multiply. This process continues. 

So the coefficients of the quotient are: 2 , 0 , 1

So the quotient is: 2x²+0x+1=2x²+1 

Remainder = -3