(10×2-13x+12)÷(5x-1)

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

5x | – | 1 | 10×2 | – | 13x | + | 12 |

Divide the highest order term in the dividend 10×2 by the highest order term in divisor 5x.

2x | |||||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 |

Multiply the new quotient term by the divisor.

2x | |||||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

+ | 10×2 | – | 2x |

The expression needs to be subtracted from the dividend, so change all the signs in 10×2-2x

2x | |||||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x |

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

2x | |||||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x | ||||||

– | 11x |

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

2x | |||||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x | ||||||

– | 11x | + | 12 |

Divide the highest order term in the dividend -11x by the highest order term in divisor 5x.

2x | – | 115 | |||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x | ||||||

– | 11x | + | 12 |

Multiply the new quotient term by the divisor.

2x | – | 115 | |||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x | ||||||

– | 11x | + | 12 | ||||||

– | 11x | + | 115 |

The expression needs to be subtracted from the dividend, so change all the signs in -11x+115

2x | – | 115 | |||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x | ||||||

– | 11x | + | 12 | ||||||

+ | 11x | – | 115 |

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

2x | – | 115 | |||||||

5x | – | 1 | 10×2 | – | 13x | + | 12 | ||

– | 10×2 | + | 2x | ||||||

– | 11x | + | 12 | ||||||

+ | 11x | – | 115 | ||||||

+ | 495 |

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

2x-115+495(5x-1)

Divide (10x^2-13x+12)÷(5x-1)