4×2-2x-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.

x | + | 1 | 4×2 | – | 2x | – | 5 |

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

4x | |||||||||

x | + | 1 | 4×2 | – | 2x | – | 5 |

Multiply the new quotient term by the divisor.

4x | |||||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

+ | 4×2 | + | 4x |

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

4x | |||||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x |

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

4x | |||||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x | ||||||

– | 6x |

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

4x | |||||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x | ||||||

– | 6x | – | 5 |

Divide the highest order term in the dividend -6x by the highest order term in divisor x.

4x | – | 6 | |||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x | ||||||

– | 6x | – | 5 |

Multiply the new quotient term by the divisor.

4x | – | 6 | |||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x | ||||||

– | 6x | – | 5 | ||||||

– | 6x | – | 6 |

The expression needs to be subtracted from the dividend, so change all the signs in -6x-6

4x | – | 6 | |||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x | ||||||

– | 6x | – | 5 | ||||||

+ | 6x | + | 6 |

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

4x | – | 6 | |||||||

x | + | 1 | 4×2 | – | 2x | – | 5 | ||

– | 4×2 | – | 4x | ||||||

– | 6x | – | 5 | ||||||

+ | 6x | + | 6 | ||||||

+ | 1 |

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

4x-6+1x+1

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