(12m2+57+66)÷(4m+11)

Add 57 and 66.

12m2+1234m+11

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

4m | + | 11 | 12m2 | + | 0m | + | 123 |

Divide the highest order term in the dividend 12m2 by the highest order term in divisor 4m.

3m | |||||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 |

Multiply the new quotient term by the divisor.

3m | |||||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

+ | 12m2 | + | 33m |

The expression needs to be subtracted from the dividend, so change all the signs in 12m2+33m

3m | |||||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m |

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

3m | |||||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m | ||||||

– | 33m |

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

3m | |||||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m | ||||||

– | 33m | + | 123 |

Divide the highest order term in the dividend -33m by the highest order term in divisor 4m.

3m | – | 334 | |||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m | ||||||

– | 33m | + | 123 |

Multiply the new quotient term by the divisor.

3m | – | 334 | |||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m | ||||||

– | 33m | + | 123 | ||||||

– | 33m | – | 3634 |

The expression needs to be subtracted from the dividend, so change all the signs in -33m-3634

3m | – | 334 | |||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m | ||||||

– | 33m | + | 123 | ||||||

+ | 33m | + | 3634 |

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

3m | – | 334 | |||||||

4m | + | 11 | 12m2 | + | 0m | + | 123 | ||

– | 12m2 | – | 33m | ||||||

– | 33m | + | 123 | ||||||

+ | 33m | + | 3634 | ||||||

+ | 8554 |

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

3m-334+8554(4m+11)

Divide (12m^2+57+66)÷(4m+11)