3×3-3×2-2x-8x-2

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

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 |

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

3×2 | |||||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 |

Multiply the new quotient term by the divisor.

3×2 | |||||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

+ | 3×3 | – | 6×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 3×3-6×2

3×2 | |||||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 |

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

3×2 | |||||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 |

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

3×2 | |||||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x |

Divide the highest order term in the dividend 3×2 by the highest order term in divisor x.

3×2 | + | 3x | |||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x |

Multiply the new quotient term by the divisor.

3×2 | + | 3x | |||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

+ | 3×2 | – | 6x |

The expression needs to be subtracted from the dividend, so change all the signs in 3×2-6x

3×2 | + | 3x | |||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x |

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

3×2 | + | 3x | |||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x | ||||||||

+ | 4x |

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

3×2 | + | 3x | |||||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x | ||||||||

+ | 4x | – | 8 |

Divide the highest order term in the dividend 4x by the highest order term in divisor x.

3×2 | + | 3x | + | 4 | |||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x | ||||||||

+ | 4x | – | 8 |

Multiply the new quotient term by the divisor.

3×2 | + | 3x | + | 4 | |||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x | ||||||||

+ | 4x | – | 8 | ||||||||

+ | 4x | – | 8 |

The expression needs to be subtracted from the dividend, so change all the signs in 4x-8

3×2 | + | 3x | + | 4 | |||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x | ||||||||

+ | 4x | – | 8 | ||||||||

– | 4x | + | 8 |

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

3×2 | + | 3x | + | 4 | |||||||

x | – | 2 | 3×3 | – | 3×2 | – | 2x | – | 8 | ||

– | 3×3 | + | 6×2 | ||||||||

+ | 3×2 | – | 2x | ||||||||

– | 3×2 | + | 6x | ||||||||

+ | 4x | – | 8 | ||||||||

– | 4x | + | 8 | ||||||||

0 |

Since the remander is 0, the final answer is the quotient.

3×2+3x+4

Divide (3x^3-3x^2-2x-8)/(x-2)