12×4-1×3-24×2+26x-84×2+5x-4

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

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 |

Divide the highest order term in the dividend 12×4 by the highest order term in divisor 4×2.

3×2 | |||||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 |

Multiply the new quotient term by the divisor.

3×2 | |||||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

+ | 12×4 | + | 15×3 | – | 12×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 12×4+15×3-12×2

3×2 | |||||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 |

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

3×2 | |||||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 |

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

3×2 | |||||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x |

Divide the highest order term in the dividend -16×3 by the highest order term in divisor 4×2.

3×2 | – | 4x | |||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x |

Multiply the new quotient term by the divisor.

3×2 | – | 4x | |||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

– | 16×3 | – | 20×2 | + | 16x |

The expression needs to be subtracted from the dividend, so change all the signs in -16×3-20×2+16x

3×2 | – | 4x | |||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x |

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

3×2 | – | 4x | |||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x | ||||||||||

+ | 8×2 | + | 10x |

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

3×2 | – | 4x | |||||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x | ||||||||||

+ | 8×2 | + | 10x | – | 8 |

Divide the highest order term in the dividend 8×2 by the highest order term in divisor 4×2.

3×2 | – | 4x | + | 2 | |||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x | ||||||||||

+ | 8×2 | + | 10x | – | 8 |

Multiply the new quotient term by the divisor.

3×2 | – | 4x | + | 2 | |||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x | ||||||||||

+ | 8×2 | + | 10x | – | 8 | ||||||||||

+ | 8×2 | + | 10x | – | 8 |

The expression needs to be subtracted from the dividend, so change all the signs in 8×2+10x-8

3×2 | – | 4x | + | 2 | |||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x | ||||||||||

+ | 8×2 | + | 10x | – | 8 | ||||||||||

– | 8×2 | – | 10x | + | 8 |

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

3×2 | – | 4x | + | 2 | |||||||||||

4×2 | + | 5x | – | 4 | 12×4 | – | 1×3 | – | 24×2 | + | 26x | – | 8 | ||

– | 12×4 | – | 15×3 | + | 12×2 | ||||||||||

– | 16×3 | – | 12×2 | + | 26x | ||||||||||

+ | 16×3 | + | 20×2 | – | 16x | ||||||||||

+ | 8×2 | + | 10x | – | 8 | ||||||||||

– | 8×2 | – | 10x | + | 8 | ||||||||||

0 |

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

3×2-4x+2

Divide (12x^4-1x^3-24x^2+26x-8)/(4x^2+5x-4)