I see that you have over thirty postings.
By now you should understand that this is not a homework service
So you need to either post some of your work on a problem or explain what you do not understand about the question.
1. f(x) = x^3  7x^2 + 17x  15 ; 2+i
2. f(x) = x^3 + 6x + 20 ; 13i
3. g(x) = x^4  6x^3 + 6x^2 + 24x  40 ; 3+i
4. g(x) = x^3  3x^2 + 9x  7 ; 1
Apologies. While these questions are indeed a few from my homework, I did not ask this simply to find the answers and get done with it, as I am sure is the source of mathhelpforum wanting to make clear that they are not a homework service. I figure that if I understand these 4, I will be able to do all of them. As per request, I'll work through as much as I can of the first one.
x^3  7x^2 + 17x  15; 2+i
By the Conjugate Pair Theorem, both 2+i and 2i are zeroes of the function. The goal is to synthetically divide by the zeroes until the function is down to a quadratic.
2+i 1 7 17 15

 1 2+i 93i 19+3i

1 5+i 83i 4+3i
Since 2+i is given as a zero, the remainder should be zero, and not (4+3i) Using 2i gives similar results. I'm not understanding what I'm doing wrong.