Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
| + | – | – | + | – |
Divide the highest order term in the dividend by the highest order term in divisor .
| + | – | – | + | – |
Multiply the new quotient term by the divisor.
| + | – | – | + | – | |||||||||
| + | + | – |
The expression needs to be subtracted from the dividend, so change all the signs in
| + | – | – | + | – | |||||||||
| – | – | + |
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 by the highest order term in divisor .
| – | |||||||||||||
| + | – | – | + | – | |||||||||
| – | – | + | |||||||||||
| – | + | – |
Multiply the new quotient term by the divisor.
| – | |||||||||||||
| + | – | – | + | – | |||||||||
| – | – | + | |||||||||||
| – | + | – | |||||||||||
| – | + | + |
The expression needs to be subtracted from the dividend, so change all the signs in
| – | |||||||||||||
| + | – | – | + | – | |||||||||
| – | – | + | |||||||||||
| – | + | – | |||||||||||
| + | – | – |
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.
Divide Using Long Polynomial Division (3x^3-2x^2-5)/(x^2-4)
