(12×4+17×3+8x-40)÷(x+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 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 |

Divide the highest order term in the dividend 12×4 by the highest order term in divisor x.

12×3 | |||||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 |

Multiply the new quotient term by the divisor.

12×3 | |||||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

+ | 12×4 | + | 24×3 |

The expression needs to be subtracted from the dividend, so change all the signs in 12×4+24×3

12×3 | |||||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 |

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

12×3 | |||||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 |

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

12×3 | |||||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 |

Divide the highest order term in the dividend -7×3 by the highest order term in divisor x.

12×3 | – | 7×2 | |||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 |

Multiply the new quotient term by the divisor.

12×3 | – | 7×2 | |||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

– | 7×3 | – | 14×2 |

The expression needs to be subtracted from the dividend, so change all the signs in -7×3-14×2

12×3 | – | 7×2 | |||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 |

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

12×3 | – | 7×2 | |||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 |

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

12×3 | – | 7×2 | |||||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x |

Divide the highest order term in the dividend 14×2 by the highest order term in divisor x.

12×3 | – | 7×2 | + | 14x | |||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x |

Multiply the new quotient term by the divisor.

12×3 | – | 7×2 | + | 14x | |||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

+ | 14×2 | + | 28x |

The expression needs to be subtracted from the dividend, so change all the signs in 14×2+28x

12×3 | – | 7×2 | + | 14x | |||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x |

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

12×3 | – | 7×2 | + | 14x | |||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x | ||||||||||

– | 20x |

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

12×3 | – | 7×2 | + | 14x | |||||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x | ||||||||||

– | 20x | – | 40 |

Divide the highest order term in the dividend -20x by the highest order term in divisor x.

12×3 | – | 7×2 | + | 14x | – | 20 | |||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x | ||||||||||

– | 20x | – | 40 |

Multiply the new quotient term by the divisor.

12×3 | – | 7×2 | + | 14x | – | 20 | |||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x | ||||||||||

– | 20x | – | 40 | ||||||||||

– | 20x | – | 40 |

The expression needs to be subtracted from the dividend, so change all the signs in -20x-40

12×3 | – | 7×2 | + | 14x | – | 20 | |||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x | ||||||||||

– | 20x | – | 40 | ||||||||||

+ | 20x | + | 40 |

12×3 | – | 7×2 | + | 14x | – | 20 | |||||||

x | + | 2 | 12×4 | + | 17×3 | + | 0x2 | + | 8x | – | 40 | ||

– | 12×4 | – | 24×3 | ||||||||||

– | 7×3 | + | 0x2 | ||||||||||

+ | 7×3 | + | 14×2 | ||||||||||

+ | 14×2 | + | 8x | ||||||||||

– | 14×2 | – | 28x | ||||||||||

– | 20x | – | 40 | ||||||||||

+ | 20x | + | 40 | ||||||||||

0 |

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

12×3-7×2+14x-20

Divide (12x^4+17x^3+8x-40)÷(x+2)