(5×2+14x+3)÷(x+2)

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

x | + | 2 | 5×2 | + | 14x | + | 3 |

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

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

x | + | 2 | 5×2 | + | 14x | + | 3 |

Multiply the new quotient term by the divisor.

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

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

+ | 5×2 | + | 10x |

The expression needs to be subtracted from the dividend, so change all the signs in 5×2+10x

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

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x |

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

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

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x | ||||||

+ | 4x |

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

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

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x | ||||||

+ | 4x | + | 3 |

Divide the highest order term in the dividend 4x by the highest order term in divisor x.

5x | + | 4 | |||||||

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x | ||||||

+ | 4x | + | 3 |

Multiply the new quotient term by the divisor.

5x | + | 4 | |||||||

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x | ||||||

+ | 4x | + | 3 | ||||||

+ | 4x | + | 8 |

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

5x | + | 4 | |||||||

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x | ||||||

+ | 4x | + | 3 | ||||||

– | 4x | – | 8 |

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

5x | + | 4 | |||||||

x | + | 2 | 5×2 | + | 14x | + | 3 | ||

– | 5×2 | – | 10x | ||||||

+ | 4x | + | 3 | ||||||

– | 4x | – | 8 | ||||||

– | 5 |

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

5x+4-5x+2

Divide (5x^2+14x+3)÷(x+2)