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 term 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.
| + | + | ||||||||||
| – | – | + | – | ||||||||
| – | + | ||||||||||
| + | – | ||||||||||
| – | + | ||||||||||
Since the remander is , the final answer is the quotient.
Since the final term in the resulting expression is not a fraction, the remainder is .
Find the Remainder (x^3-5x^2+2x-10)/(x-5)