(x^3-5x^2+2x-10) / (x-5)
You can actually do this as long division (I will use )‾ as the division symbol)
x-5 )‾x3 - 5x2 + 2x - 10 x goes into x3 x2 times
-(x3 - 5x2) Now multiply x2 by x-5
0 0 2x - 10 Subtract and bring down the
-(2x - 10) next terms and do it again
0 0 Finally we we take our terms
x2 + 2 from the top for our new equation.
Time to check our work
(Remember FOIL - First Outer Inner Last)
(x2 + 2)(x-5) (x2)(x) = x3 (x2)(-5) = -5x2
x3 - 5x2 + 2x - 10 (2)(x) = 2x (2)(-5) = -10
There we go!
(x3 - 5x2 + 2x - 10)/(x-5) = x2 + 2