3y3-y+4y-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 | 3y3 | + | 0y2 | – | y | + | 4 |

Divide the highest order term in the dividend 3y3 by the highest order term in divisor y.

3y2 | |||||||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 |

Multiply the new quotient term by the divisor.

3y2 | |||||||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

+ | 3y3 | – | 6y2 |

The expression needs to be subtracted from the dividend, so change all the signs in 3y3-6y2

3y2 | |||||||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 |

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

3y2 | |||||||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 |

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

3y2 | |||||||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y |

Divide the highest order term in the dividend 6y2 by the highest order term in divisor y.

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

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y |

Multiply the new quotient term by the divisor.

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

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

+ | 6y2 | – | 12y |

The expression needs to be subtracted from the dividend, so change all the signs in 6y2-12y

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

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y |

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

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

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y | ||||||||

+ | 11y |

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

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

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y | ||||||||

+ | 11y | + | 4 |

Divide the highest order term in the dividend 11y by the highest order term in divisor y.

3y2 | + | 6y | + | 11 | |||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y | ||||||||

+ | 11y | + | 4 |

Multiply the new quotient term by the divisor.

3y2 | + | 6y | + | 11 | |||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y | ||||||||

+ | 11y | + | 4 | ||||||||

+ | 11y | – | 22 |

The expression needs to be subtracted from the dividend, so change all the signs in 11y-22

3y2 | + | 6y | + | 11 | |||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y | ||||||||

+ | 11y | + | 4 | ||||||||

– | 11y | + | 22 |

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

3y2 | + | 6y | + | 11 | |||||||

y | – | 2 | 3y3 | + | 0y2 | – | y | + | 4 | ||

– | 3y3 | + | 6y2 | ||||||||

+ | 6y2 | – | y | ||||||||

– | 6y2 | + | 12y | ||||||||

+ | 11y | + | 4 | ||||||||

– | 11y | + | 22 | ||||||||

+ | 26 |

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

3y2+6y+11+26y-2

Divide (3y^3-y+4)/(y-2)