(y3-y2-8y+3)÷(y+2)

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

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 |

Divide the highest order term in the dividend y3 by the highest order term in divisor y.

y2 | |||||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 |

Multiply the new quotient term by the divisor.

y2 | |||||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

+ | y3 | + | 2y2 |

The expression needs to be subtracted from the dividend, so change all the signs in y3+2y2

y2 | |||||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 |

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

y2 | |||||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 |

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

y2 | |||||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y |

Divide the highest order term in the dividend -3y2 by the highest order term in divisor y.

y2 | – | 3y | |||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y |

Multiply the new quotient term by the divisor.

y2 | – | 3y | |||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

– | 3y2 | – | 6y |

The expression needs to be subtracted from the dividend, so change all the signs in -3y2-6y

y2 | – | 3y | |||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y |

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

y2 | – | 3y | |||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y | ||||||||

– | 2y |

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

y2 | – | 3y | |||||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y | ||||||||

– | 2y | + | 3 |

Divide the highest order term in the dividend -2y by the highest order term in divisor y.

y2 | – | 3y | – | 2 | |||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y | ||||||||

– | 2y | + | 3 |

Multiply the new quotient term by the divisor.

y2 | – | 3y | – | 2 | |||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y | ||||||||

– | 2y | + | 3 | ||||||||

– | 2y | – | 4 |

The expression needs to be subtracted from the dividend, so change all the signs in -2y-4

y2 | – | 3y | – | 2 | |||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y | ||||||||

– | 2y | + | 3 | ||||||||

+ | 2y | + | 4 |

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

y2 | – | 3y | – | 2 | |||||||

y | + | 2 | y3 | – | y2 | – | 8y | + | 3 | ||

– | y3 | – | 2y2 | ||||||||

– | 3y2 | – | 8y | ||||||||

+ | 3y2 | + | 6y | ||||||||

– | 2y | + | 3 | ||||||||

+ | 2y | + | 4 | ||||||||

+ | 7 |

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

y2-3y-2+7y+2

Divide (y^3-y^2-8y+3)÷(y+2)