(5×2+18x+6)÷(x+3)

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

x | + | 3 | 5×2 | + | 18x | + | 6 |

Divide the highest order term in the dividend 5×2 by the highest order term in divisor x.

5x | |||||||||

x | + | 3 | 5×2 | + | 18x | + | 6 |

Multiply the new quotient term by the divisor.

5x | |||||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

+ | 5×2 | + | 15x |

The expression needs to be subtracted from the dividend, so change all the signs in 5×2+15x

5x | |||||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x |

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

5x | |||||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x | ||||||

+ | 3x |

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

5x | |||||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x | ||||||

+ | 3x | + | 6 |

Divide the highest order term in the dividend 3x by the highest order term in divisor x.

5x | + | 3 | |||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x | ||||||

+ | 3x | + | 6 |

Multiply the new quotient term by the divisor.

5x | + | 3 | |||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x | ||||||

+ | 3x | + | 6 | ||||||

+ | 3x | + | 9 |

The expression needs to be subtracted from the dividend, so change all the signs in 3x+9

5x | + | 3 | |||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x | ||||||

+ | 3x | + | 6 | ||||||

– | 3x | – | 9 |

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

5x | + | 3 | |||||||

x | + | 3 | 5×2 | + | 18x | + | 6 | ||

– | 5×2 | – | 15x | ||||||

+ | 3x | + | 6 | ||||||

– | 3x | – | 9 | ||||||

– | 3 |

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

5x+3-3x+3

Divide (5x^2+18x+6)÷(x+3)