(10×3+8×2+13x+4)÷(5x-1)

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

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 |

Divide the highest order term in the dividend 10×3 by the highest order term in divisor 5x.

2×2 | |||||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 |

Multiply the new quotient term by the divisor.

2×2 | |||||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

+ | 10×3 | – | 2×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 10×3-2×2

2×2 | |||||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 |

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

2×2 | |||||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 |

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

2×2 | |||||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x |

Divide the highest order term in the dividend 10×2 by the highest order term in divisor 5x.

2×2 | + | 2x | |||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x |

Multiply the new quotient term by the divisor.

2×2 | + | 2x | |||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

+ | 10×2 | – | 2x |

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

2×2 | + | 2x | |||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x |

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

2×2 | + | 2x | |||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x | ||||||||

+ | 15x |

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

2×2 | + | 2x | |||||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x | ||||||||

+ | 15x | + | 4 |

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

2×2 | + | 2x | + | 3 | |||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x | ||||||||

+ | 15x | + | 4 |

Multiply the new quotient term by the divisor.

2×2 | + | 2x | + | 3 | |||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x | ||||||||

+ | 15x | + | 4 | ||||||||

+ | 15x | – | 3 |

The expression needs to be subtracted from the dividend, so change all the signs in 15x-3

2×2 | + | 2x | + | 3 | |||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x | ||||||||

+ | 15x | + | 4 | ||||||||

– | 15x | + | 3 |

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

2×2 | + | 2x | + | 3 | |||||||

5x | – | 1 | 10×3 | + | 8×2 | + | 13x | + | 4 | ||

– | 10×3 | + | 2×2 | ||||||||

+ | 10×2 | + | 13x | ||||||||

– | 10×2 | + | 2x | ||||||||

+ | 15x | + | 4 | ||||||||

– | 15x | + | 3 | ||||||||

+ | 7 |

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

2×2+2x+3+75x-1

Divide (10x^3+8x^2+13x+4)÷(5x-1)