(12m2+57+66)÷(4m+11)
Add 57 and 66.
12m2+1234m+11
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 4m | + | 11 | 12m2 | + | 0m | + | 123 |
Divide the highest order term in the dividend 12m2 by the highest order term in divisor 4m.
| 3m | |||||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 |
Multiply the new quotient term by the divisor.
| 3m | |||||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| + | 12m2 | + | 33m |
The expression needs to be subtracted from the dividend, so change all the signs in 12m2+33m
| 3m | |||||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 3m | |||||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m | ||||||
| – | 33m |
Pull the next terms from the original dividend down into the current dividend.
| 3m | |||||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m | ||||||
| – | 33m | + | 123 |
Divide the highest order term in the dividend -33m by the highest order term in divisor 4m.
| 3m | – | 334 | |||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m | ||||||
| – | 33m | + | 123 |
Multiply the new quotient term by the divisor.
| 3m | – | 334 | |||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m | ||||||
| – | 33m | + | 123 | ||||||
| – | 33m | – | 3634 |
The expression needs to be subtracted from the dividend, so change all the signs in -33m-3634
| 3m | – | 334 | |||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m | ||||||
| – | 33m | + | 123 | ||||||
| + | 33m | + | 3634 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 3m | – | 334 | |||||||
| 4m | + | 11 | 12m2 | + | 0m | + | 123 | ||
| – | 12m2 | – | 33m | ||||||
| – | 33m | + | 123 | ||||||
| + | 33m | + | 3634 | ||||||
| + | 8554 |
The final answer is the quotient plus the remainder over the divisor.
3m-334+8554(4m+11)
Divide (12m^2+57+66)÷(4m+11)
