Question 8522
This is a little hard to describe. You need to look up synthetic division to most easily solve this problem.
Basically, it is this: you divide x+3 into the polynomial. 
x+3 divides (x^3+5x^2-6x+10) x^2 times. x^2 times x+3 is x^3+3x^2. You subtract this from the polynomial and you have 2x^2-6x+10 remaining. 
x+3 divides into (2x^2-6x+10) 2x times. 2x times x+3 is 2x^2+6x. You subtract this from the polynomial you had left and you get -12x+10 remaining.
x+3 divides into (-12x+10) -12 times. -12 times x+3 is -12x-36. You subtract this from the polynomial you had left and you get 46 remaining. 
You cannot divide x+3 into 46, so the remainder is 46/(x+3).