Azr2119
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# Identify the oblique asymptote of f(x) = quantity 2 x squared minus 5 x plus 2 over quantity x minus 3.

$\bf f(x)=\cfrac{2x^2-5x+2}{x-3}\impliedby \begin{array}{llll} \textit{now, we can do a quick synthetic}\\ \textit{division, since the divisor is}\\ x-3 \end{array}\\\\ -------------------------------\\\\ \begin{array}{r|rrrrl} 3&&2&-5&2\\ &&&6&3\\ --&&--&--&--\\ &&2&1&\boxed{5}&\leftarrow remainder \end{array}\\\\ -------------------------------\\\\ \textit{so the quotient is }2x+1\impliedby \textit{oblique asymptote}\implies y=2x+1$