12×5-35×4+31×3-11×2+4x-63×2-5x+3

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

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 |

Divide the highest order term in the dividend 12×5 by the highest order term in divisor 3×2.

4×3 | |||||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 |

Multiply the new quotient term by the divisor.

4×3 | |||||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

+ | 12×5 | – | 20×4 | + | 12×3 |

The expression needs to be subtracted from the dividend, so change all the signs in 12×5-20×4+12×3

4×3 | |||||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 |

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

4×3 | |||||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 |

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

4×3 | |||||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 |

Divide the highest order term in the dividend -15×4 by the highest order term in divisor 3×2.

4×3 | – | 5×2 | |||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 |

Multiply the new quotient term by the divisor.

4×3 | – | 5×2 | |||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

– | 15×4 | + | 25×3 | – | 15×2 |

The expression needs to be subtracted from the dividend, so change all the signs in -15×4+25×3-15×2

4×3 | – | 5×2 | |||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 |

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

4×3 | – | 5×2 | |||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 |

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

4×3 | – | 5×2 | |||||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x |

Divide the highest order term in the dividend -6×3 by the highest order term in divisor 3×2.

4×3 | – | 5×2 | – | 2x | |||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x |

Multiply the new quotient term by the divisor.

4×3 | – | 5×2 | – | 2x | |||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

– | 6×3 | + | 10×2 | – | 6x |

The expression needs to be subtracted from the dividend, so change all the signs in -6×3+10×2-6x

4×3 | – | 5×2 | – | 2x | |||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x |

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

4×3 | – | 5×2 | – | 2x | |||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x | ||||||||||||

– | 6×2 | + | 10x |

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

4×3 | – | 5×2 | – | 2x | |||||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x | ||||||||||||

– | 6×2 | + | 10x | – | 6 |

Divide the highest order term in the dividend -6×2 by the highest order term in divisor 3×2.

4×3 | – | 5×2 | – | 2x | – | 2 | |||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x | ||||||||||||

– | 6×2 | + | 10x | – | 6 |

Multiply the new quotient term by the divisor.

4×3 | – | 5×2 | – | 2x | – | 2 | |||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x | ||||||||||||

– | 6×2 | + | 10x | – | 6 | ||||||||||||

– | 6×2 | + | 10x | – | 6 |

The expression needs to be subtracted from the dividend, so change all the signs in -6×2+10x-6

4×3 | – | 5×2 | – | 2x | – | 2 | |||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x | ||||||||||||

– | 6×2 | + | 10x | – | 6 | ||||||||||||

+ | 6×2 | – | 10x | + | 6 |

4×3 | – | 5×2 | – | 2x | – | 2 | |||||||||||

3×2 | – | 5x | + | 3 | 12×5 | – | 35×4 | + | 31×3 | – | 11×2 | + | 4x | – | 6 | ||

– | 12×5 | + | 20×4 | – | 12×3 | ||||||||||||

– | 15×4 | + | 19×3 | – | 11×2 | ||||||||||||

+ | 15×4 | – | 25×3 | + | 15×2 | ||||||||||||

– | 6×3 | + | 4×2 | + | 4x | ||||||||||||

+ | 6×3 | – | 10×2 | + | 6x | ||||||||||||

– | 6×2 | + | 10x | – | 6 | ||||||||||||

+ | 6×2 | – | 10x | + | 6 | ||||||||||||

0 |

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

4×3-5×2-2x-2

Divide (12x^5-35x^4+31x^3-11x^2+4x-6)/(3x^2-5x+3)