What is longdivision ((243x^5-1))/((3x+1)) ?

The solution to longdivision ((243x^5-1))/((3x+1)) is 81x^4-27x^3+9x^2-3x+1-2/(3x+1)

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longdivision ((243x^5-1))/((3x+1))

long division

\frac{( 243 x ^{5} - 1 )}{( 3 x + 1 )}

81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + 1 - \frac{2}{3 x + 1}

Solution steps

\frac{( 243 x ^{5} - 1 )}{( 3 x + 1 )}

Divide

\frac{243 x ^{5} - 1}{3 x + 1} : \frac{243 x ^{5} - 1}{3 x + 1} = 81 x^{4} + \frac{- 81 x ^{4} - 1}{3 x + 1}

= 81 x^{4} + \frac{- 81 x ^{4} - 1}{3 x + 1}

Divide

\frac{- 81 x ^{4} - 1}{3 x + 1} : \frac{- 81 x ^{4} - 1}{3 x + 1} = - 27 x^{3} + \frac{27 x ^{3} - 1}{3 x + 1}

= 81 x^{4} - 27 x^{3} + \frac{27 x ^{3} - 1}{3 x + 1}

Divide

\frac{27 x ^{3} - 1}{3 x + 1} : \frac{27 x ^{3} - 1}{3 x + 1} = 9 x^{2} + \frac{- 9 x ^{2} - 1}{3 x + 1}

= 81 x^{4} - 27 x^{3} + 9 x^{2} + \frac{- 9 x ^{2} - 1}{3 x + 1}

Divide

\frac{- 9 x ^{2} - 1}{3 x + 1} : \frac{- 9 x ^{2} - 1}{3 x + 1} = - 3 x + \frac{3 x - 1}{3 x + 1}

= 81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + \frac{3 x - 1}{3 x + 1}

Divide

\frac{3 x - 1}{3 x + 1} : \frac{3 x - 1}{3 x + 1} = 1 + \frac{- 2}{3 x + 1}

= 81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + 1 + \frac{- 2}{3 x + 1}

Simplify

= 81 x^{4} - 27 x^{3} + 9 x^{2} - 3 x + 1 - \frac{2}{3 x + 1}

\frac{( x ^{2} + 1 )}{( x + 1 )}

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

\frac{( x ^{4} - x ^{2} + 1 )}{( 1 - x )}

\frac{( 6 a ^{2} - 7 a + 5 )}{( 2 a - 3 )}

\frac{( 2 x ^{2} + 5 x - 7 )}{( x - 2 )}

What is longdivision ((243x^5-1))/((3x+1)) ?
The solution to longdivision ((243x^5-1))/((3x+1)) is 81x^4-27x^3+9x^2-3x+1-2/(3x+1)