15×2+24x+15x+3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 5x | + | 3 | 15×2 | + | 24x | + | 1 |
Divide the highest order term in the dividend 15×2 by the highest order term in divisor 5x.
| 3x | |||||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 |
Multiply the new quotient term by the divisor.
| 3x | |||||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| + | 15×2 | + | 9x |
The expression needs to be subtracted from the dividend, so change all the signs in 15×2+9x
| 3x | |||||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 3x | |||||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x | ||||||
| + | 15x |
Pull the next terms from the original dividend down into the current dividend.
| 3x | |||||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x | ||||||
| + | 15x | + | 1 |
Divide the highest order term in the dividend 15x by the highest order term in divisor 5x.
| 3x | + | 3 | |||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x | ||||||
| + | 15x | + | 1 |
Multiply the new quotient term by the divisor.
| 3x | + | 3 | |||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x | ||||||
| + | 15x | + | 1 | ||||||
| + | 15x | + | 9 |
The expression needs to be subtracted from the dividend, so change all the signs in 15x+9
| 3x | + | 3 | |||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x | ||||||
| + | 15x | + | 1 | ||||||
| – | 15x | – | 9 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 3x | + | 3 | |||||||
| 5x | + | 3 | 15×2 | + | 24x | + | 1 | ||
| – | 15×2 | – | 9x | ||||||
| + | 15x | + | 1 | ||||||
| – | 15x | – | 9 | ||||||
| – | 8 |
The final answer is the quotient plus the remainder over the divisor.
3x+3-85x+3
Divide (15x^2+24x+1)/(5x+3)
