6×2+21x+62x+5

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

2x | + | 5 | 6×2 | + | 21x | + | 6 |

Divide the highest order term in the dividend 6×2 by the highest order term in divisor 2x.

3x | |||||||||

2x | + | 5 | 6×2 | + | 21x | + | 6 |

Multiply the new quotient term by the divisor.

3x | |||||||||

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

+ | 6×2 | + | 15x |

The expression needs to be subtracted from the dividend, so change all the signs in 6×2+15x

3x | |||||||||

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x |

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

3x | |||||||||

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x | ||||||

+ | 6x |

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

3x | |||||||||

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x | ||||||

+ | 6x | + | 6 |

Divide the highest order term in the dividend 6x by the highest order term in divisor 2x.

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

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x | ||||||

+ | 6x | + | 6 |

Multiply the new quotient term by the divisor.

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

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x | ||||||

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

+ | 6x | + | 15 |

The expression needs to be subtracted from the dividend, so change all the signs in 6x+15

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

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x | ||||||

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

– | 6x | – | 15 |

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

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

2x | + | 5 | 6×2 | + | 21x | + | 6 | ||

– | 6×2 | – | 15x | ||||||

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

– | 6x | – | 15 | ||||||

– | 9 |

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

3x+3-92x+5

Divide (6x^2+21x+6)/(2x+5)