Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

+ | + | - | + | + |

Divide the highest order term in the dividend <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> by the highest order term in divisor <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

+ | + | - | + | + |

Multiply the new quotient term by the divisor.

+ | + | - | + | + | |||||||||

+ | + | + |

The expression needs to be subtracted from the dividend, so change all the signs in <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi></mstyle></math>

+ | + | - | + | + | |||||||||

- | - | - |

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

+ | + | - | + | + | |||||||||

- | - | - | |||||||||||

- | + |

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

+ | + | - | + | + | |||||||||

- | - | - | |||||||||||

- | + | + |

Divide the highest order term in the dividend <math><mstyle displaystyle="true"><mo>-</mo><mn>7</mn><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by the highest order term in divisor <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

- | |||||||||||||

+ | + | - | + | + | |||||||||

- | - | - | |||||||||||

- | + | + |

Multiply the new quotient term by the divisor.

- | |||||||||||||

+ | + | - | + | + | |||||||||

- | - | - | |||||||||||

- | + | + | |||||||||||

- | - | - |

The expression needs to be subtracted from the dividend, so change all the signs in <math><mstyle displaystyle="true"><mo>-</mo><mn>7</mn><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mfrac><mrow><mn>7</mn><mi>b</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

- | |||||||||||||

+ | + | - | + | + | |||||||||

- | - | - | |||||||||||

- | + | + | |||||||||||

+ | + | + |

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

- | |||||||||||||

+ | + | - | + | + | |||||||||

- | - | - | |||||||||||

- | + | + | |||||||||||

+ | + | + | |||||||||||

+ | + |

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

Do you know how to Divide Using Long Polynomial Division (2b^3-6b^2+8b)÷(2b^2+b+1)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.