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

+ | + | + |

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

+ | + | + |

Multiply the new quotient term by the divisor.

+ | + | + | |||||||

+ | + |

The expression needs to be subtracted from the dividend, so change all the signs in

+ | + | + | |||||||

– | – |

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

+ | + | + | |||||||

– | – | ||||||||

+ |

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

+ | + | + | |||||||

– | – | ||||||||

+ | + |

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

+ | |||||||||

+ | + | + | |||||||

– | – | ||||||||

+ | + |

Multiply the new quotient term by the divisor.

+ | |||||||||

+ | + | + | |||||||

– | – | ||||||||

+ | + | ||||||||

+ | + |

The expression needs to be subtracted from the dividend, so change all the signs in

+ | |||||||||

+ | + | + | |||||||

– | – | ||||||||

+ | + | ||||||||

– | – |

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

+ | |||||||||

+ | + | + | |||||||

– | – | ||||||||

+ | + | ||||||||

– | – | ||||||||

– |

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

Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

Find the Remainder (6x^2+37x+31)÷(x+5)