3×3+8×2-10x-24x+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 | 3×3 | + | 8×2 | – | 10x | – | 24 |

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

3×2 | |||||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 |

Multiply the new quotient term by the divisor.

3×2 | |||||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

+ | 3×3 | + | 12×2 |

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

3×2 | |||||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 |

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

3×2 | |||||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 |

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

3×2 | |||||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x |

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

3×2 | – | 4x | |||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x |

Multiply the new quotient term by the divisor.

3×2 | – | 4x | |||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

– | 4×2 | – | 16x |

The expression needs to be subtracted from the dividend, so change all the signs in -4×2-16x

3×2 | – | 4x | |||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x |

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

3×2 | – | 4x | |||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x | ||||||||

+ | 6x |

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

3×2 | – | 4x | |||||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x | ||||||||

+ | 6x | – | 24 |

Divide the highest order term in the dividend 6x by the highest order term in divisor x.

3×2 | – | 4x | + | 6 | |||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x | ||||||||

+ | 6x | – | 24 |

Multiply the new quotient term by the divisor.

3×2 | – | 4x | + | 6 | |||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x | ||||||||

+ | 6x | – | 24 | ||||||||

+ | 6x | + | 24 |

The expression needs to be subtracted from the dividend, so change all the signs in 6x+24

3×2 | – | 4x | + | 6 | |||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x | ||||||||

+ | 6x | – | 24 | ||||||||

– | 6x | – | 24 |

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

3×2 | – | 4x | + | 6 | |||||||

x | + | 4 | 3×3 | + | 8×2 | – | 10x | – | 24 | ||

– | 3×3 | – | 12×2 | ||||||||

– | 4×2 | – | 10x | ||||||||

+ | 4×2 | + | 16x | ||||||||

+ | 6x | – | 24 | ||||||||

– | 6x | – | 24 | ||||||||

– | 48 |

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

3×2-4x+6-48x+4

Divide (3x^3+8x^2-10x-24)/(x+4)