z2-27z-3

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

z | – | 3 | z2 | + | 0z | – | 27 |

Divide the highest order term in the dividend z2 by the highest order term in divisor z.

z | |||||||||

z | – | 3 | z2 | + | 0z | – | 27 |

Multiply the new quotient term by the divisor.

z | |||||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

+ | z2 | – | 3z |

The expression needs to be subtracted from the dividend, so change all the signs in z2-3z

z | |||||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z |

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

z | |||||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z | ||||||

+ | 3z |

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

z | |||||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z | ||||||

+ | 3z | – | 27 |

Divide the highest order term in the dividend 3z by the highest order term in divisor z.

z | + | 3 | |||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z | ||||||

+ | 3z | – | 27 |

Multiply the new quotient term by the divisor.

z | + | 3 | |||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z | ||||||

+ | 3z | – | 27 | ||||||

+ | 3z | – | 9 |

The expression needs to be subtracted from the dividend, so change all the signs in 3z-9

z | + | 3 | |||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z | ||||||

+ | 3z | – | 27 | ||||||

– | 3z | + | 9 |

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

z | + | 3 | |||||||

z | – | 3 | z2 | + | 0z | – | 27 | ||

– | z2 | + | 3z | ||||||

+ | 3z | – | 27 | ||||||

– | 3z | + | 9 | ||||||

– | 18 |

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

z+3-18z-3

Divide (z^2-27)/(z-3)