6×2+21x+62x+5
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 2x | + | 5 | 6×2 | + | 21x | + | 6 |
Divide the highest order term in the dividend 6×2 by the highest order term in divisor 2x.
| 3x | |||||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 |
Multiply the new quotient term by the divisor.
| 3x | |||||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| + | 6×2 | + | 15x |
The expression needs to be subtracted from the dividend, so change all the signs in 6×2+15x
| 3x | |||||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 3x | |||||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x | ||||||
| + | 6x |
Pull the next terms from the original dividend down into the current dividend.
| 3x | |||||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x | ||||||
| + | 6x | + | 6 |
Divide the highest order term in the dividend 6x by the highest order term in divisor 2x.
| 3x | + | 3 | |||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x | ||||||
| + | 6x | + | 6 |
Multiply the new quotient term by the divisor.
| 3x | + | 3 | |||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x | ||||||
| + | 6x | + | 6 | ||||||
| + | 6x | + | 15 |
The expression needs to be subtracted from the dividend, so change all the signs in 6x+15
| 3x | + | 3 | |||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x | ||||||
| + | 6x | + | 6 | ||||||
| – | 6x | – | 15 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 3x | + | 3 | |||||||
| 2x | + | 5 | 6×2 | + | 21x | + | 6 | ||
| – | 6×2 | – | 15x | ||||||
| + | 6x | + | 6 | ||||||
| – | 6x | – | 15 | ||||||
| – | 9 |
The final answer is the quotient plus the remainder over the divisor.
3x+3-92x+5
Divide (6x^2+21x+6)/(2x+5)
