x4-x3-14×2+7x-4x-4

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

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 |

Divide the highest order term in the dividend x4 by the highest order term in divisor x.

x3 | |||||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 |

Multiply the new quotient term by the divisor.

x3 | |||||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

+ | x4 | – | 4×3 |

The expression needs to be subtracted from the dividend, so change all the signs in x4-4×3

x3 | |||||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 |

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

x3 | |||||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 |

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

x3 | |||||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 |

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

x3 | + | 3×2 | |||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 |

Multiply the new quotient term by the divisor.

x3 | + | 3×2 | |||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

+ | 3×3 | – | 12×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 3×3-12×2

x3 | + | 3×2 | |||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 |

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

x3 | + | 3×2 | |||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 |

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

x3 | + | 3×2 | |||||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x |

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

x3 | + | 3×2 | – | 2x | |||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x |

Multiply the new quotient term by the divisor.

x3 | + | 3×2 | – | 2x | |||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

– | 2×2 | + | 8x |

The expression needs to be subtracted from the dividend, so change all the signs in -2×2+8x

x3 | + | 3×2 | – | 2x | |||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x |

x3 | + | 3×2 | – | 2x | |||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x | ||||||||||

– | x |

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

x3 | + | 3×2 | – | 2x | |||||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x | ||||||||||

– | x | – | 4 |

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

x3 | + | 3×2 | – | 2x | – | 1 | |||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x | ||||||||||

– | x | – | 4 |

Multiply the new quotient term by the divisor.

x3 | + | 3×2 | – | 2x | – | 1 | |||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x | ||||||||||

– | x | – | 4 | ||||||||||

– | x | + | 4 |

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

x3 | + | 3×2 | – | 2x | – | 1 | |||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x | ||||||||||

– | x | – | 4 | ||||||||||

+ | x | – | 4 |

x3 | + | 3×2 | – | 2x | – | 1 | |||||||

x | – | 4 | x4 | – | x3 | – | 14×2 | + | 7x | – | 4 | ||

– | x4 | + | 4×3 | ||||||||||

+ | 3×3 | – | 14×2 | ||||||||||

– | 3×3 | + | 12×2 | ||||||||||

– | 2×2 | + | 7x | ||||||||||

+ | 2×2 | – | 8x | ||||||||||

– | x | – | 4 | ||||||||||

+ | x | – | 4 | ||||||||||

– | 8 |

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

x3+3×2-2x-1-8x-4

Divide (x^4-x^3-14x^2+7x-4)/(x-4)