6c4-12c2+18c+196c+6

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

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 |

Divide the highest order term in the dividend 6c4 by the highest order term in divisor 6c.

c3 | |||||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 |

Multiply the new quotient term by the divisor.

c3 | |||||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

+ | 6c4 | + | 6c3 |

The expression needs to be subtracted from the dividend, so change all the signs in 6c4+6c3

c3 | |||||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 |

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

c3 | |||||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 |

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

c3 | |||||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 |

Divide the highest order term in the dividend -6c3 by the highest order term in divisor 6c.

c3 | – | c2 | |||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 |

Multiply the new quotient term by the divisor.

c3 | – | c2 | |||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

– | 6c3 | – | 6c2 |

The expression needs to be subtracted from the dividend, so change all the signs in -6c3-6c2

c3 | – | c2 | |||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 |

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

c3 | – | c2 | |||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 |

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

c3 | – | c2 | |||||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c |

Divide the highest order term in the dividend -6c2 by the highest order term in divisor 6c.

c3 | – | c2 | – | c | |||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c |

Multiply the new quotient term by the divisor.

c3 | – | c2 | – | c | |||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

– | 6c2 | – | 6c |

The expression needs to be subtracted from the dividend, so change all the signs in -6c2-6c

c3 | – | c2 | – | c | |||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c |

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

c3 | – | c2 | – | c | |||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c | ||||||||||

+ | 24c |

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

c3 | – | c2 | – | c | |||||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c | ||||||||||

+ | 24c | + | 19 |

Divide the highest order term in the dividend 24c by the highest order term in divisor 6c.

c3 | – | c2 | – | c | + | 4 | |||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c | ||||||||||

+ | 24c | + | 19 |

Multiply the new quotient term by the divisor.

c3 | – | c2 | – | c | + | 4 | |||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c | ||||||||||

+ | 24c | + | 19 | ||||||||||

+ | 24c | + | 24 |

The expression needs to be subtracted from the dividend, so change all the signs in 24c+24

c3 | – | c2 | – | c | + | 4 | |||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c | ||||||||||

+ | 24c | + | 19 | ||||||||||

– | 24c | – | 24 |

c3 | – | c2 | – | c | + | 4 | |||||||

6c | + | 6 | 6c4 | + | 0c3 | – | 12c2 | + | 18c | + | 19 | ||

– | 6c4 | – | 6c3 | ||||||||||

– | 6c3 | – | 12c2 | ||||||||||

+ | 6c3 | + | 6c2 | ||||||||||

– | 6c2 | + | 18c | ||||||||||

+ | 6c2 | + | 6c | ||||||||||

+ | 24c | + | 19 | ||||||||||

– | 24c | – | 24 | ||||||||||

– | 5 |

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

c3-c2-c+4-56c+6

Divide (6c^4-12c^2+18c+19)/(6c+6)