x^5+a^5 is divided by x+a
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Sia ? 6 years, 4 months ago
x5 + a5 by x + a
We stop here since the remainder is zero,
So,
quotient {tex}= x ^ { 4 } - a x ^ { 3 } + a ^ { 2 } x ^ { 2 } - a ^ { 3 } x + a ^ { 4 }{/tex}
remainder = 0
Therefore,
{tex}\text { Quotient } \times \text { Divisor } + \text { Remainder }{/tex}
{tex}= \left( x ^ { 4 } - a x ^ { 3 } + a ^ { 2 } x ^ { 2 } - a ^ { 3 } x + a ^ { 4 } \right) ( x + a ) + 0{/tex}
{tex}= x ^ { 5 } + a x ^ { 4 } - a x ^ { 4 } - a ^ { 2 } x ^ { 3 } + a ^ { 2 } x ^ { 3 }{/tex}
{tex}+ a ^ { 3 } x ^ { 2 } - a ^ { 3 } x ^ { 2 } - a ^ { 4 } x + a ^ { 4 } x + a ^ { 5 }{/tex}
{tex}= x ^ { 5 } + a ^ { 5 }{/tex}
= Dividend
Therefore, the division algorithm is verified.
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