One difference between synthetic division of polynomials and long division of polynomials is the fact that in synthetic division you must "add down," but in long division you must "subtract down." think about each process, and decide why this difference occurs. write a short paragraph explaining why this difference occurs, to the best of your ability.

Well if you look at the two methods you can clearly see that you add downwards for synthetic and you subtract downwards for long division. Long division is also known as Remainder theorem, this is when you divide and subtract the terms to get a remainder, if the remainders is 0 then the divisor is a factor. Synthetic is merely just another technique for solving cubics and higher order polynomials