$x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ by $x^{3} + 1$

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Solution

${by} x^{5} + x^{4} + x^{3} + x^{2} + x + 1$

Quotient = ${x2+x+1} x^{3} + 1$

Remainder = 0

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Similar questions

\int (x + x^{2} + x^{3} + x^{4})

x \neq - 1

\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1}

x \neq - 1

\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1} = 1

x_{1}, x_{2}, x_{3}, x_{4}, x_{5}

\sqrt{x_{1} - 1} + 2 \sqrt{x_{2} - 4} + 3 \sqrt{x_{3} - 9} + 4 \sqrt{x_{4} - 16} + 5 \sqrt{x_{5} - 25} = \frac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5}}{2}

\frac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5}}{2}

x

(1 - x) (1 + x + x^{2} + x^{3} + x^{4})

= \frac{31}{32} .

1 + x + x^{2} + x^{3} + x^{4} + x^{5}

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