Identify the oblique asymptotes of f(x)=2x^2-5x+2 over x-3

QUESTION POSTED AT 01/06/2020 - 04:45 PM

Answered by admin AT 01/06/2020 - 04:45 PM

\bf \cfrac{2x^2-5x+2}{x-3}\qquad 
\begin{array}{r|rrrrll}
3&2&-5&2\\
&&6&3\\
--&--&--&--\\
&2&1&5
\end{array}
\\\\\\
quotient=\underline{2x+1}\qquad remainder=5
\\\\\\
\textit{thus oblique asymptote is }y=\underline{2x+1}

oblique/slant asymptotes occur when the degree of the numerator is exactly 1 greater than that of the denominator

and the oblique asymptote occurs at the quotient of the rational expression, notice, since the denominator is just x - 3, doing a quick synthetic division will do to get the quotient.
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