Question

Use synthetic division to divide the polynomial 2x^3 – 12x – 5 by x + 4,

Write the quotient polynomial and the remainder. [Be careful – notice that there is no x2 term.]. Show work.

Answer 1

Synthetic division is the same as long polynomial division, except that we write down only the coefficients, and not the complete terms. For this to be valid, any missing term must be compensated by a 0 (read the note [Be careful...]).
Synthetic division is very similar to numeric long division that we are used to, except each digit is replaced by a number, positive or negative. The layout is almost the same.
You can read up
http://en.wikipedia.org/wiki/Polynomial_long_division
for an example.
The work is not difficult, but difficult to do a nice layout by posting.
Try it out and see if you have difficulties.

Answer 2

The quotient is 2x³-8x+20 with a remainder of -85.

Answer 3

erratum:
The quotient is 2x²-8x+20 with a remainder of -85.

Answer 4

76