8m2+4m-122m+1

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

2m | + | 1 | 8m2 | + | 4m | – | 12 |

Divide the highest order term in the dividend 8m2 by the highest order term in divisor 2m.

4m | |||||||||

2m | + | 1 | 8m2 | + | 4m | – | 12 |

Multiply the new quotient term by the divisor.

4m | |||||||||

2m | + | 1 | 8m2 | + | 4m | – | 12 | ||

+ | 8m2 | + | 4m |

The expression needs to be subtracted from the dividend, so change all the signs in 8m2+4m

4m | |||||||||

2m | + | 1 | 8m2 | + | 4m | – | 12 | ||

– | 8m2 | – | 4m |

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

4m | |||||||||

2m | + | 1 | 8m2 | + | 4m | – | 12 | ||

– | 8m2 | – | 4m | ||||||

0 |

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

4m | |||||||||

2m | + | 1 | 8m2 | + | 4m | – | 12 | ||

– | 8m2 | – | 4m | ||||||

0 | – | 12 |

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

4m-122m+1

Divide (8m^2+4m-12)/(2m+1)