5×3-26×2-29x+30x-6

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

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 |

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

5×2 | |||||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 |

Multiply the new quotient term by the divisor.

5×2 | |||||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

+ | 5×3 | – | 30×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 5×3-30×2

5×2 | |||||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 |

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

5×2 | |||||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 |

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

5×2 | |||||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x |

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

5×2 | + | 4x | |||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x |

Multiply the new quotient term by the divisor.

5×2 | + | 4x | |||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

+ | 4×2 | – | 24x |

The expression needs to be subtracted from the dividend, so change all the signs in 4×2-24x

5×2 | + | 4x | |||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x |

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

5×2 | + | 4x | |||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x | ||||||||

– | 5x |

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

5×2 | + | 4x | |||||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x | ||||||||

– | 5x | + | 30 |

Divide the highest order term in the dividend -5x by the highest order term in divisor x.

5×2 | + | 4x | – | 5 | |||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x | ||||||||

– | 5x | + | 30 |

Multiply the new quotient term by the divisor.

5×2 | + | 4x | – | 5 | |||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x | ||||||||

– | 5x | + | 30 | ||||||||

– | 5x | + | 30 |

The expression needs to be subtracted from the dividend, so change all the signs in -5x+30

5×2 | + | 4x | – | 5 | |||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x | ||||||||

– | 5x | + | 30 | ||||||||

+ | 5x | – | 30 |

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

5×2 | + | 4x | – | 5 | |||||||

x | – | 6 | 5×3 | – | 26×2 | – | 29x | + | 30 | ||

– | 5×3 | + | 30×2 | ||||||||

+ | 4×2 | – | 29x | ||||||||

– | 4×2 | + | 24x | ||||||||

– | 5x | + | 30 | ||||||||

+ | 5x | – | 30 | ||||||||

0 |

Since the remander is 0, the final answer is the quotient.

5×2+4x-5

Divide (5x^3-26x^2-29x+30)/(x-6)