Problem 258: Let’s divide 
by 
.
Solution: Write the problem as a long division problem.
![\[x-8 \overline{)2x^3 - 11x^2 - 41x + 9}\]](https://1problematatime.com/wp-content/ql-cache/quicklatex.com-84162d85fee62334ee393fd9ceda0c74_l3.png "Rendered by QuickLaTeX.com")
When doing long division, we make sure that the dividend is in descending order of degree. In this case, it is.
We start the long division by dividing 
(the first term in the dividend) by 
(the first term in the divisor). Then we repeat the process.
![\[\begin{matrix}2x^2 + 5x - 1 \\ \qquad x-8 \overline{)2x^3 - 11x^2 - 41x + 9} \\ \underline{-(2x^3 - 16x^2)} \\ \qquad \qquad \qquad \qquad 5x^2 - 41x + 9 \\ \qquad \qquad \qquad \underline{-(5x^2 - 40x)} \\ \qquad \qquad \qquad \qquad \qquad \quad -x + 9 \\ \qquad \qquad \qquad \qquad \qquad \quad \underline{-(-x+8)} \\ \qquad \qquad \qquad \qquad \qquad \qquad \qquad 1 \end{matrix}\]](https://1problematatime.com/wp-content/ql-cache/quicklatex.com-f9592da609d272bf185b20a4d204c087_l3.png "Rendered by QuickLaTeX.com")
The result is given by the quotient and the remainder over the divisor. That is,
![\[2x^2 + 5x -1 + \frac{1}{x-8}.\]](https://1problematatime.com/wp-content/ql-cache/quicklatex.com-7e476f7c0ede20b91e4b4ae1111353aa_l3.png "Rendered by QuickLaTeX.com")
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