Question

Divide (x5 -y 5 ) by (x-y) using the method of long division.

Answer 1

Answer:

this is the answer.

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Answer 2

Quotient of polynomial division is$\bf {x}^{4} + {x}^{3}y + {x}^{2} {y}^{2} + x {y}^{3} + {y}^{4}$

Remainder is zero.

Given:

• ${x}^{5} - {y}^{5}$ and $(x - y)$

To find:

• Divide the polynomial by long division method.

Solution:

Write the polynomial under division sign.

$x - y \: ) \: {x}^{5} \: \: \: \: \: \: \: \: \: - {y}^{5} \: ( {x}^{4} + {x}^{3}y + {x}^{2} {y}^{2} + x {y}^{3} + {y}^{4} \\ \: \: \: \: \: {x}^{5} - {x}^{4} y \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ( - ) \: \: ( + ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ {x}^{4} y \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ {x}^{4} y - {x}^{3} {y}^{2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ ( - ) \: \: ( + ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - \\ {x}^{3} {y}^{2} \: \: \: \: \: \: \: \: \: \: \: \\ {x}^{3} {y}^{2} - {x}^{2} {y}^{3} \\ ( - ) \: \: ( + ) \\ - - - - - \\ {x}^{2} {y}^{3} \: \: \: \: \: \: \: \: \: \\ {x}^{2} {y}^{3} - x {y}^{4} \\ ( - ) \: \: ( + ) \\ - - - - - \\ x {y}^{4} - {y}^{5} \\ x {y}^{4} - {y}^{5} \\ ( - ) \: \: ( + ) \\ - - - - - \\ 0 \\ - - - - -$

Thus,

Quotient of polynomial division is $\bf {x}^{4} + {x}^{3}y + {x}^{2} {y}^{2} + x {y}^{3} + {y}^{4}$

Remainder is zero.

Learn more:

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