Answer:
[tex]\boxed{\text{Quotient = } 2x^{2} - 10x + 49; \text{remainder = } -244}[/tex]
Step-by-step explanation:
Perhaps the best way to solve this problem is to use synthetic division.
[tex]\begin{array}{rrrrr}-5| & 2 & 0 & -1 & 1\\|& & -10 & 50 & -245\\& 2 & -10 & 4 & -244\\\end{array}\\[/tex]
Thus,
[tex]\frac{x^{3} - x + 1 }{x + 5} = 2x^{2} - 10x + 49 - \frac{ 244}{x + 5 }[/tex]
The quotient is [tex]\boxed{ 2x^{2} - 10x + 49}[/tex] with a remainder of [tex]\boxed{-244}[/tex].
