What is the remainder when x^2-5x-22 is divided by x+3?
i'd also like to know how to do it so i can do the rest on my own and make sure i'm doing it right

First, you need to find the zero of x+3, which is -3
then you multiply -3×1, which equals -3
the reason why I multiplied -3×1 is because the 1 is the coefficient of x^2 but we just don't see it because we don't need to.
once we get -3 we add that to the next coefficient (-5)
-3+-5=-8
we take the sum (-8) and multiply that to -3 (the zero of x+3)
we get 24, so we add -22+24=2
-22 Is the next coefficient to come and 2 is our remainder
the new equation is: x-8 remainder 2