n2+6n+8n+3

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

n | + | 3 | n2 | + | 6n | + | 8 |

Divide the highest order term in the dividend n2 by the highest order term in divisor n.

n | |||||||||

n | + | 3 | n2 | + | 6n | + | 8 |

Multiply the new quotient term by the divisor.

n | |||||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

+ | n2 | + | 3n |

The expression needs to be subtracted from the dividend, so change all the signs in n2+3n

n | |||||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n |

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

n | |||||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n | ||||||

+ | 3n |

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

n | |||||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n | ||||||

+ | 3n | + | 8 |

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

n | + | 3 | |||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n | ||||||

+ | 3n | + | 8 |

Multiply the new quotient term by the divisor.

n | + | 3 | |||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n | ||||||

+ | 3n | + | 8 | ||||||

+ | 3n | + | 9 |

The expression needs to be subtracted from the dividend, so change all the signs in 3n+9

n | + | 3 | |||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n | ||||||

+ | 3n | + | 8 | ||||||

– | 3n | – | 9 |

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

n | + | 3 | |||||||

n | + | 3 | n2 | + | 6n | + | 8 | ||

– | n2 | – | 3n | ||||||

+ | 3n | + | 8 | ||||||

– | 3n | – | 9 | ||||||

– | 1 |

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

n+3-1n+3

Divide (n^2+6n+8)/(n+3)