(5×2+18x+6)÷(x+3)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| x | + | 3 | 5×2 | + | 18x | + | 6 |
Divide the highest order term in the dividend 5×2 by the highest order term in divisor x.
| 5x | |||||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 |
Multiply the new quotient term by the divisor.
| 5x | |||||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| + | 5×2 | + | 15x |
The expression needs to be subtracted from the dividend, so change all the signs in 5×2+15x
| 5x | |||||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 5x | |||||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x | ||||||
| + | 3x |
Pull the next terms from the original dividend down into the current dividend.
| 5x | |||||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x | ||||||
| + | 3x | + | 6 |
Divide the highest order term in the dividend 3x by the highest order term in divisor x.
| 5x | + | 3 | |||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x | ||||||
| + | 3x | + | 6 |
Multiply the new quotient term by the divisor.
| 5x | + | 3 | |||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x | ||||||
| + | 3x | + | 6 | ||||||
| + | 3x | + | 9 |
The expression needs to be subtracted from the dividend, so change all the signs in 3x+9
| 5x | + | 3 | |||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x | ||||||
| + | 3x | + | 6 | ||||||
| – | 3x | – | 9 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 5x | + | 3 | |||||||
| x | + | 3 | 5×2 | + | 18x | + | 6 | ||
| – | 5×2 | – | 15x | ||||||
| + | 3x | + | 6 | ||||||
| – | 3x | – | 9 | ||||||
| – | 3 |
The final answer is the quotient plus the remainder over the divisor.
5x+3-3x+3
Divide (5x^2+18x+6)÷(x+3)
