5×2-17x+2x-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 | 5×2 | – | 17x | + | 2 |

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

5x | |||||||||

x | – | 4 | 5×2 | – | 17x | + | 2 |

Multiply the new quotient term by the divisor.

5x | |||||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

+ | 5×2 | – | 20x |

The expression needs to be subtracted from the dividend, so change all the signs in 5×2-20x

5x | |||||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x |

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

5x | |||||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x | ||||||

+ | 3x |

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

5x | |||||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x | ||||||

+ | 3x | + | 2 |

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

5x | + | 3 | |||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x | ||||||

+ | 3x | + | 2 |

Multiply the new quotient term by the divisor.

5x | + | 3 | |||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x | ||||||

+ | 3x | + | 2 | ||||||

+ | 3x | – | 12 |

The expression needs to be subtracted from the dividend, so change all the signs in 3x-12

5x | + | 3 | |||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x | ||||||

+ | 3x | + | 2 | ||||||

– | 3x | + | 12 |

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

5x | + | 3 | |||||||

x | – | 4 | 5×2 | – | 17x | + | 2 | ||

– | 5×2 | + | 20x | ||||||

+ | 3x | + | 2 | ||||||

– | 3x | + | 12 | ||||||

+ | 14 |

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

5x+3+14x-4

Divide (5x^2-17x+2)/(x-4)