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Divide the polynomials. Your answer should be in the form $p(x)+(\frac{k}{x})$ where $p$ is a polynomial and $k$ is an integer. $\frac{x^5+6x+2}{x}$

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Composition of linear and quadratic functions: find an equation

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Q. Divide the polynomials. Your answer should be in the form

p(x)+(\frac{k}{x})

where

p

is a polynomial and

k

is an integer.

\frac{x^5+6x+2}{x}

Set up division by $x$ : Step $1$ : Start by setting up the division of the polynomial by $x$ . Divide each term of the polynomial $x^5 + 6x + 2$ by $x$ . $x^5 / x = x^4$ , $6x / x = 6$ , $2 / x$ remains as $2/x$ .
Combine division results: Step $2$ : Combine the results from the division. $\newline$ The polynomial part is $x^4 + 6$ . The remainder is $\frac{2}{x}$ .
Write final answer: Step $3$ : Write the final answer in the required format. $p(x) = x^4 + 6$ and $k = 2$ , so the answer is $x^4 + 6 + \frac{2}{x}$ .

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