Using Synthetic division to find the quotient and remainder...?

Question

Use synthetic division to find the quotient and the remainder.
(x^3 - 7x^2 + 13x + 3) divided by (x+3)

(x^3 -3x + 10) divided by (x-2)

(x^5 +32) divided by (x+2)

(x^3 + 3ix^2 - 4ix -2) divided by (x+ i)

Please explain the answers please! I'm really trying to check my work and understand how to do this stuff.....

Answer 1

Set it up as the following, then the steps are to use the variable--i.e., how many times does x (from the x+3) go into x^3...answer: x^2, then multiply and then subtract, then repeat. I'm only doing the first to show you the process as the formatting will likely be awkward anyway (ignore the periods they are space holders).

..................x^2 -10x -17 r 48
_________________
x + 3 | x^3 -7x^2 + 13x + 3
...........x^3 +3x^2 .....................(subtract)
...........-------------
..................-10x^2 + 13x .........(drop the 13x down)
................ -10x^2 - 30x ..........(multiply -10x from top times (x+3)
...................-------------------
............................... -17x + 3
............................... -17x -51
................................------------
..........................................+ 48 ( remainder )