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

– | + | + | – |

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

– | + | + | – |

Multiply the new quotient term by the divisor.

– | + | + | – | ||||||||

+ | – |

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

– | + | + | – | ||||||||

– | + |

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

– | + | + | – | ||||||||

– | + | ||||||||||

+ |

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

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + |

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

+ | |||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + |

Multiply the new quotient term by the divisor.

+ | |||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

+ | – |

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

+ | |||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + |

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

+ | |||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + | ||||||||||

+ |

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

+ | |||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + | ||||||||||

+ | – |

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

+ | + | ||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + | ||||||||||

+ | – |

Multiply the new quotient term by the divisor.

+ | + | ||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + | ||||||||||

+ | – | ||||||||||

+ | – |

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

+ | + | ||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + | ||||||||||

+ | – | ||||||||||

– | + |

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

+ | + | ||||||||||

– | + | + | – | ||||||||

– | + | ||||||||||

+ | + | ||||||||||

– | + | ||||||||||

+ | – | ||||||||||

– | + | ||||||||||

+ |

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

Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

Find the Remainder (x^3-1)/(x-4)