b3+4b2+1b+4

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

b | + | 4 | b3 | + | 4b2 | + | 0b | + | 1 |

Divide the highest order term in the dividend b3 by the highest order term in divisor b.

b2 | |||||||||||

b | + | 4 | b3 | + | 4b2 | + | 0b | + | 1 |

Multiply the new quotient term by the divisor.

b2 | |||||||||||

b | + | 4 | b3 | + | 4b2 | + | 0b | + | 1 | ||

+ | b3 | + | 4b2 |

The expression needs to be subtracted from the dividend, so change all the signs in b3+4b2

b2 | |||||||||||

b | + | 4 | b3 | + | 4b2 | + | 0b | + | 1 | ||

– | b3 | – | 4b2 |

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

b2 | |||||||||||

b | + | 4 | b3 | + | 4b2 | + | 0b | + | 1 | ||

– | b3 | – | 4b2 | ||||||||

0 |

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

b2 | |||||||||||

b | + | 4 | b3 | + | 4b2 | + | 0b | + | 1 | ||

– | b3 | – | 4b2 | ||||||||

0 | + | 0b | + | 1 |

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

b2+1b+4

Divide (b^3+4b^2+1)/(b+4)