Find the remainder $(54 m^{3} + 18 m^{2} - 27 m + 5) / (m - 3)$

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Solution

$\frac{(54 M^{3} + 18 m^{2} - 27 m + 5)}{(M - 3)}$
$m - 3) + 54 M^{3} + 18 m^{2} - 27 m + 5 (54 M^{2} + 180 M + 1513$
$+ 54 M^{3} - 162 m^{2}$
$\pm$ $+$
_________
$+ 180 M^{2} - 27 m + 5$
$+ 180 M^{2} - 540 m$
$-$ $+$
_
$+ 513 M + 5$
$+ 513 M - 1539$
$-$ $+$
_
$1543$
_________

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