(10×3-33×2+26x-15)÷(2x-5)

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

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 |

Divide the highest order term in the dividend 10×3 by the highest order term in divisor 2x.

5×2 | |||||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 |

Multiply the new quotient term by the divisor.

5×2 | |||||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

+ | 10×3 | – | 25×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 10×3-25×2

5×2 | |||||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 |

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

5×2 | |||||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 |

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

5×2 | |||||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x |

Divide the highest order term in the dividend -8×2 by the highest order term in divisor 2x.

5×2 | – | 4x | |||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x |

Multiply the new quotient term by the divisor.

5×2 | – | 4x | |||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

– | 8×2 | + | 20x |

The expression needs to be subtracted from the dividend, so change all the signs in -8×2+20x

5×2 | – | 4x | |||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x |

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

5×2 | – | 4x | |||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x | ||||||||

+ | 6x |

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

5×2 | – | 4x | |||||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x | ||||||||

+ | 6x | – | 15 |

Divide the highest order term in the dividend 6x by the highest order term in divisor 2x.

5×2 | – | 4x | + | 3 | |||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x | ||||||||

+ | 6x | – | 15 |

Multiply the new quotient term by the divisor.

5×2 | – | 4x | + | 3 | |||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x | ||||||||

+ | 6x | – | 15 | ||||||||

+ | 6x | – | 15 |

The expression needs to be subtracted from the dividend, so change all the signs in 6x-15

5×2 | – | 4x | + | 3 | |||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x | ||||||||

+ | 6x | – | 15 | ||||||||

– | 6x | + | 15 |

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

5×2 | – | 4x | + | 3 | |||||||

2x | – | 5 | 10×3 | – | 33×2 | + | 26x | – | 15 | ||

– | 10×3 | + | 25×2 | ||||||||

– | 8×2 | + | 26x | ||||||||

+ | 8×2 | – | 20x | ||||||||

+ | 6x | – | 15 | ||||||||

– | 6x | + | 15 | ||||||||

0 |

Since the remander is 0, the final answer is the quotient.

5×2-4x+3

Divide (10x^3-33x^2+26x-15)÷(2x-5)