# Algebra Examples

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.