divide (x^2-10x+30÷(x-5)

To divide (x^2-10x+30) by (x-5), you can use long division or synthetic division methods.

Long division:
_________________________
(x-5) | (x^2 - 10x + 30)
- (x^2 - 5x)
_______________
-5x + 30
- (-5x + 25)
_______________
5

The quotient is 5.

Synthetic division:

First, set up the problem in synthetic division format by setting x-5 equal to zero and solving for x:

x - 5 = 0
x = 5

Next, use the value of x=5 to perform synthetic division:

5 | 1 -10 30
5 -25
___________
1 - 5 5

The result of synthetic division is 1x - 5 with a remainder of 5.

Thus, (x^2-10x+30) ÷ (x-5) = 5 with a remainder of 5.