4×2-72x-3

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

2x | – | 3 | 4×2 | + | 0x | – | 7 |

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

2x | |||||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 |

Multiply the new quotient term by the divisor.

2x | |||||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

+ | 4×2 | – | 6x |

The expression needs to be subtracted from the dividend, so change all the signs in 4×2-6x

2x | |||||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x |

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

2x | |||||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x | ||||||

+ | 6x |

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

2x | |||||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x | ||||||

+ | 6x | – | 7 |

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

2x | + | 3 | |||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x | ||||||

+ | 6x | – | 7 |

Multiply the new quotient term by the divisor.

2x | + | 3 | |||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x | ||||||

+ | 6x | – | 7 | ||||||

+ | 6x | – | 9 |

The expression needs to be subtracted from the dividend, so change all the signs in 6x-9

2x | + | 3 | |||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x | ||||||

+ | 6x | – | 7 | ||||||

– | 6x | + | 9 |

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

2x | + | 3 | |||||||

2x | – | 3 | 4×2 | + | 0x | – | 7 | ||

– | 4×2 | + | 6x | ||||||

+ | 6x | – | 7 | ||||||

– | 6x | + | 9 | ||||||

+ | 2 |

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

2x+3+22x-3

Divide (4x^2-7)/(2x-3)