p3-6p-1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 |

Divide the highest order term in the dividend p3 by the highest order term in divisor p.

p2 | |||||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 |

Multiply the new quotient term by the divisor.

p2 | |||||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

+ | p3 | – | p2 |

The expression needs to be subtracted from the dividend, so change all the signs in p3-p2

p2 | |||||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

p2 | |||||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 |

Pull the next terms from the original dividend down into the current dividend.

p2 | |||||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p |

Divide the highest order term in the dividend p2 by the highest order term in divisor p.

p2 | + | p | |||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p |

Multiply the new quotient term by the divisor.

p2 | + | p | |||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

+ | p2 | – | p |

The expression needs to be subtracted from the dividend, so change all the signs in p2-p

p2 | + | p | |||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

p2 | + | p | |||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p | ||||||||

+ | p |

Pull the next terms from the original dividend down into the current dividend.

p2 | + | p | |||||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p | ||||||||

+ | p | – | 6 |

Divide the highest order term in the dividend p by the highest order term in divisor p.

p2 | + | p | + | 1 | |||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p | ||||||||

+ | p | – | 6 |

Multiply the new quotient term by the divisor.

p2 | + | p | + | 1 | |||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p | ||||||||

+ | p | – | 6 | ||||||||

+ | p | – | 1 |

The expression needs to be subtracted from the dividend, so change all the signs in p-1

p2 | + | p | + | 1 | |||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p | ||||||||

+ | p | – | 6 | ||||||||

– | p | + | 1 |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

p2 | + | p | + | 1 | |||||||

p | – | 1 | p3 | + | 0p2 | + | 0p | – | 6 | ||

– | p3 | + | p2 | ||||||||

+ | p2 | + | 0p | ||||||||

– | p2 | + | p | ||||||||

+ | p | – | 6 | ||||||||

– | p | + | 1 | ||||||||

– | 5 |

The final answer is the quotient plus the remainder over the divisor.

p2+p+1-5p-1

Divide (p^3-6)/(p-1)