ANSWER
[tex] \frac{ - 3 {x}^{3} - 2 {x}^{2} - x - 2}{x - 2} = - 3 {x}^{2} - 8x - 17 - \frac{36}{x - 2} [/tex]
EXPLANATION
We want to divide
[tex] - 3 {x}^{3} - 2 {x}^{2} - x - 2[/tex]
by
[tex]x - 2[/tex]
We perform synthetic division to obtain:
The remainder to be -36.
The quotient is
[tex] - 3 {x}^{2} - 8x - 17[/tex]
Therefore,
[tex] \frac{ - 3 {x}^{3} - 2 {x}^{2} - x - 2}{x - 2} = - 3 {x}^{2} - 8x - 17 - \frac{36}{x - 2} [/tex]
