15×2+24x+15x+3

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

5x | + | 3 | 15×2 | + | 24x | + | 1 |

Divide the highest order term in the dividend 15×2 by the highest order term in divisor 5x.

3x | |||||||||

5x | + | 3 | 15×2 | + | 24x | + | 1 |

Multiply the new quotient term by the divisor.

3x | |||||||||

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

+ | 15×2 | + | 9x |

The expression needs to be subtracted from the dividend, so change all the signs in 15×2+9x

3x | |||||||||

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x |

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

3x | |||||||||

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x | ||||||

+ | 15x |

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

3x | |||||||||

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x | ||||||

+ | 15x | + | 1 |

Divide the highest order term in the dividend 15x by the highest order term in divisor 5x.

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

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x | ||||||

+ | 15x | + | 1 |

Multiply the new quotient term by the divisor.

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

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x | ||||||

+ | 15x | + | 1 | ||||||

+ | 15x | + | 9 |

The expression needs to be subtracted from the dividend, so change all the signs in 15x+9

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

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x | ||||||

+ | 15x | + | 1 | ||||||

– | 15x | – | 9 |

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

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

5x | + | 3 | 15×2 | + | 24x | + | 1 | ||

– | 15×2 | – | 9x | ||||||

+ | 15x | + | 1 | ||||||

– | 15x | – | 9 | ||||||

– | 8 |

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

3x+3-85x+3

Divide (15x^2+24x+1)/(5x+3)