(4k3-30k2-106k+64)÷(k-10)

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

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 |

Divide the highest order term in the dividend 4k3 by the highest order term in divisor k.

4k2 | |||||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 |

Multiply the new quotient term by the divisor.

4k2 | |||||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

+ | 4k3 | – | 40k2 |

The expression needs to be subtracted from the dividend, so change all the signs in 4k3-40k2

4k2 | |||||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 |

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

4k2 | |||||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 |

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

4k2 | |||||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k |

Divide the highest order term in the dividend 10k2 by the highest order term in divisor k.

4k2 | + | 10k | |||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k |

Multiply the new quotient term by the divisor.

4k2 | + | 10k | |||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

+ | 10k2 | – | 100k |

The expression needs to be subtracted from the dividend, so change all the signs in 10k2-100k

4k2 | + | 10k | |||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k |

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

4k2 | + | 10k | |||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k | ||||||||

– | 6k |

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

4k2 | + | 10k | |||||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k | ||||||||

– | 6k | + | 64 |

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

4k2 | + | 10k | – | 6 | |||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k | ||||||||

– | 6k | + | 64 |

Multiply the new quotient term by the divisor.

4k2 | + | 10k | – | 6 | |||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k | ||||||||

– | 6k | + | 64 | ||||||||

– | 6k | + | 60 |

The expression needs to be subtracted from the dividend, so change all the signs in -6k+60

4k2 | + | 10k | – | 6 | |||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k | ||||||||

– | 6k | + | 64 | ||||||||

+ | 6k | – | 60 |

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

4k2 | + | 10k | – | 6 | |||||||

k | – | 10 | 4k3 | – | 30k2 | – | 106k | + | 64 | ||

– | 4k3 | + | 40k2 | ||||||||

+ | 10k2 | – | 106k | ||||||||

– | 10k2 | + | 100k | ||||||||

– | 6k | + | 64 | ||||||||

+ | 6k | – | 60 | ||||||||

+ | 4 |

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

4k2+10k-6+4k-10

Divide (4k^3-30k^2-106k+64)÷(k-10)