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 .

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Multiply the new quotient term by the divisor.

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+ | + |

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

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

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– |

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

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– | – | ||||||||||

– | + |

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 .

– | + | ||||||||||

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

– | – | ||||||||||

– | + | ||||||||||

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+ | + |

Multiply the new quotient term by the divisor.

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

– | – | ||||||||||

– | + | ||||||||||

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

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

+ | + |

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.

– | + | ||||||||||

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

– | – | ||||||||||

– | + | ||||||||||

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+ |

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

Divide (25w^3+10w^2+37w+38)÷(5w+4)