(7×3-8×2-13x+2)÷(7x-1)

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

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 |

Divide the highest order term in the dividend 7×3 by the highest order term in divisor 7x.

x2 | |||||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 |

Multiply the new quotient term by the divisor.

x2 | |||||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

+ | 7×3 | – | x2 |

The expression needs to be subtracted from the dividend, so change all the signs in 7×3-x2

x2 | |||||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 |

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

x2 | |||||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 |

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

x2 | |||||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x |

Divide the highest order term in the dividend -7×2 by the highest order term in divisor 7x.

x2 | – | x | |||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x |

Multiply the new quotient term by the divisor.

x2 | – | x | |||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

– | 7×2 | + | x |

The expression needs to be subtracted from the dividend, so change all the signs in -7×2+x

x2 | – | x | |||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x |

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

x2 | – | x | |||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x | ||||||||

– | 14x |

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

x2 | – | x | |||||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x | ||||||||

– | 14x | + | 2 |

Divide the highest order term in the dividend -14x by the highest order term in divisor 7x.

x2 | – | x | – | 2 | |||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x | ||||||||

– | 14x | + | 2 |

Multiply the new quotient term by the divisor.

x2 | – | x | – | 2 | |||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x | ||||||||

– | 14x | + | 2 | ||||||||

– | 14x | + | 2 |

The expression needs to be subtracted from the dividend, so change all the signs in -14x+2

x2 | – | x | – | 2 | |||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x | ||||||||

– | 14x | + | 2 | ||||||||

+ | 14x | – | 2 |

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

x2 | – | x | – | 2 | |||||||

7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||

– | 7×3 | + | x2 | ||||||||

– | 7×2 | – | 13x | ||||||||

+ | 7×2 | – | x | ||||||||

– | 14x | + | 2 | ||||||||

+ | 14x | – | 2 | ||||||||

0 |

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

x2-x-2

Divide (7x^3-8x^2-13x+2)÷(7x-1)