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Division of a Polynomial by a Monomial

Find Remainde...

Question

Find Remainder :
$\frac{(27)^{999}}{7}$

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Solution

We have,
$\begin{matrix} \frac{{(27)}^{999}}{7} = {(28 - 1)}^{999} = {(27)}^{999} {(28 - 1)}^{999} =^{999} C_{0} {(28)}^{999} -^{999} C_{1} {(28)}^{998} +^{999} C_{2} {(28)}^{997} + . . . . . . . . . . . . . . . . . +^{999} C_{998} {(28)}^{1} -^{999} C_{999} = 28 λ - 1 = 28 λ^{'} + 27 = 7 m + 6 T h u s r e m a i n d e r i s 6 w h e n d i v i d e d b y 7. \end{matrix}$

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