4×3-6×2-8x+12x-4

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

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 |

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

2×2 | |||||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 |

Multiply the new quotient term by the divisor.

2×2 | |||||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

+ | 4×3 | – | 8×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 4×3-8×2

2×2 | |||||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 |

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

2×2 | |||||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 |

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

2×2 | |||||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x |

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

2×2 | + | x | |||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x |

Multiply the new quotient term by the divisor.

2×2 | + | x | |||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

+ | 2×2 | – | 4x |

The expression needs to be subtracted from the dividend, so change all the signs in 2×2-4x

2×2 | + | x | |||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x |

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

2×2 | + | x | |||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x | ||||||||

– | 4x |

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

2×2 | + | x | |||||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x | ||||||||

– | 4x | + | 1 |

Divide the highest order term in the dividend -4x by the highest order term in divisor 2x.

2×2 | + | x | – | 2 | |||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x | ||||||||

– | 4x | + | 1 |

Multiply the new quotient term by the divisor.

2×2 | + | x | – | 2 | |||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x | ||||||||

– | 4x | + | 1 | ||||||||

– | 4x | + | 8 |

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

2×2 | + | x | – | 2 | |||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x | ||||||||

– | 4x | + | 1 | ||||||||

+ | 4x | – | 8 |

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

2×2 | + | x | – | 2 | |||||||

2x | – | 4 | 4×3 | – | 6×2 | – | 8x | + | 1 | ||

– | 4×3 | + | 8×2 | ||||||||

+ | 2×2 | – | 8x | ||||||||

– | 2×2 | + | 4x | ||||||||

– | 4x | + | 1 | ||||||||

+ | 4x | – | 8 | ||||||||

– | 7 |

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

2×2+x-2-72x-4

Divide (4x^3-6x^2-8x+1)/(2x-4)