First of all, we can simplify the dividend:
[tex]-2x+11x^2-23x+20=11x^2-25x+20[/tex] so we can rewrite our problem as 11x^2-25x+20 divided by [tex]x^2-3x+4[/tex].
Now, to find the result of the division, we are going to perform long division as you can see in the attached image.
We can conclude that the result of of dividing [tex]11x^2-25x+20[/tex] by [tex]x^2-3x+4[/tex] is [tex]11[/tex] with a remainder of [tex]8x-24[/tex], or in other notation: [tex] \frac{-2x+11x^2-23x+20}{x^2-3x+4} =11+ \frac{8x-24}{x^2-3x+4} [/tex]
