Answer:
[tex]-3x^2+29x-150+\frac{946x^2-341x-756}{x^3+6x^2-3x-5}[/tex] is the answer. See steps below.
Step-by-step explanation:
[tex]\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}\\\\-3x^5+11x^4+33x^3-26x^2-36x-6\\\\\mathrm{and\:the\:divisor\:}x^3+6x^2-3x-5:\\\\\mathrm{Quotient}=\frac{-3x^5}{x^3}=-3x^2\\\\\mathrm{Multiply\:}x^3+6x^2-3x-5\mathrm{\:by\:}-3x^2\:\:\rightarrow\:\:-3x^5-18x^4+9x^3+15x^2\\\\\mathrm{Subtract\:}-3x^5-18x^4+9x^3+15x^2\mathrm{\:from\:}-3x^5+11x^4+33x^3-26x^2-36x-6\mathrm{\:to\:get\:new\:remainder}.\\\\\mathrm{Remainder}=29x^4+24x^3-41x^2-36x-6[/tex]
[tex]=-3x^2+\frac{29x^4+24x^3-41x^2-36x-6}{x^3+6x^2-3x-5}[/tex]
Repeat the steps and you will reach a point where no further division is possible.
[tex]=-3x^2+29x-150+\frac{946x^2-341x-756}{x^3+6x^2-3x-5}[/tex]
