x^5+a^5 is divided by x+a

1.	x^5+a^5 is divided by x+a
Answer» x5 + a5 by x + aWe stop here since the remainder is zero,So,quotient\xa0{tex}= x ^ { 4 } - a x ^ { 3 } + a ^ { 2 } x ^ { 2 } - a ^ { 3 } x + a ^ { 4 }{/tex}remainder = 0Therefore,{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}= DividendTherefore, the division algorithm is verified.

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