9×3-33×2-272x-320x+1

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

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 |

Divide the highest order term in the dividend 9×3 by the highest order term in divisor x.

9×2 | |||||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 |

Multiply the new quotient term by the divisor.

9×2 | |||||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

+ | 9×3 | + | 9×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 9×3+9×2

9×2 | |||||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 |

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

9×2 | |||||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 |

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

9×2 | |||||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x |

Divide the highest order term in the dividend -42×2 by the highest order term in divisor x.

9×2 | – | 42x | |||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x |

Multiply the new quotient term by the divisor.

9×2 | – | 42x | |||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

– | 42×2 | – | 42x |

The expression needs to be subtracted from the dividend, so change all the signs in -42×2-42x

9×2 | – | 42x | |||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x |

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

9×2 | – | 42x | |||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x | ||||||||

– | 230x |

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

9×2 | – | 42x | |||||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x | ||||||||

– | 230x | – | 320 |

Divide the highest order term in the dividend -230x by the highest order term in divisor x.

9×2 | – | 42x | – | 230 | |||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x | ||||||||

– | 230x | – | 320 |

Multiply the new quotient term by the divisor.

9×2 | – | 42x | – | 230 | |||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x | ||||||||

– | 230x | – | 320 | ||||||||

– | 230x | – | 230 |

The expression needs to be subtracted from the dividend, so change all the signs in -230x-230

9×2 | – | 42x | – | 230 | |||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x | ||||||||

– | 230x | – | 320 | ||||||||

+ | 230x | + | 230 |

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

9×2 | – | 42x | – | 230 | |||||||

x | + | 1 | 9×3 | – | 33×2 | – | 272x | – | 320 | ||

– | 9×3 | – | 9×2 | ||||||||

– | 42×2 | – | 272x | ||||||||

+ | 42×2 | + | 42x | ||||||||

– | 230x | – | 320 | ||||||||

+ | 230x | + | 230 | ||||||||

– | 90 |

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

9×2-42x-230-90x+1

Divide (9x^3-33x^2-272x-320)/(x+1)