5×4-10×2+1-3×3+10×2+500

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

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 |

Divide the highest order term in the dividend 5×4 by the highest order term in divisor -3×3.

– | 5×3 | ||||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 |

Multiply the new quotient term by the divisor.

– | 5×3 | ||||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

+ | 5×4 | – | 50×33 | + | 0 | – | 2500×3 |

The expression needs to be subtracted from the dividend, so change all the signs in 5×4-50×33+0-2500×3

– | 5×3 | ||||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 |

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

– | 5×3 | ||||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 | ||||||||||

+ | 50×33 | – | 10×2 | + | 2500×3 |

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

– | 5×3 | ||||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 | ||||||||||

+ | 50×33 | – | 10×2 | + | 2500×3 | + | 1 |

Divide the highest order term in the dividend 50×33 by the highest order term in divisor -3×3.

– | 5×3 | – | 509 | ||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 | ||||||||||

+ | 50×33 | – | 10×2 | + | 2500×3 | + | 1 |

Multiply the new quotient term by the divisor.

– | 5×3 | – | 509 | ||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 | ||||||||||

+ | 50×33 | – | 10×2 | + | 2500×3 | + | 1 | ||||||||||

+ | 50×33 | – | 500×29 | + | 0 | – | 250009 |

The expression needs to be subtracted from the dividend, so change all the signs in 50×33-500×29+0-250009

– | 5×3 | – | 509 | ||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 | ||||||||||

+ | 50×33 | – | 10×2 | + | 2500×3 | + | 1 | ||||||||||

– | 50×33 | + | 500×29 | – | 0 | + | 250009 |

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

– | 5×3 | – | 509 | ||||||||||||||

– | 3×3 | + | 10×2 | + | 0x | + | 500 | 5×4 | + | 0x3 | – | 10×2 | + | 0x | + | 1 | |

– | 5×4 | + | 50×33 | – | 0 | + | 2500×3 | ||||||||||

+ | 50×33 | – | 10×2 | + | 2500×3 | + | 1 | ||||||||||

– | 50×33 | + | 500×29 | – | 0 | + | 250009 | ||||||||||

+ | 410×29 | + | 2500×3 | + | 250099 |

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

-5×3-509+410×29+2500×3+250099-3×3+10×2+500

Divide (5x^4-10x^2+1)/(-3x^3+10x^2+500)