4×2-72x-3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 2x | – | 3 | 4×2 | + | 0x | – | 7 |
Divide the highest order term in the dividend 4×2 by the highest order term in divisor 2x.
| 2x | |||||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 |
Multiply the new quotient term by the divisor.
| 2x | |||||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| + | 4×2 | – | 6x |
The expression needs to be subtracted from the dividend, so change all the signs in 4×2-6x
| 2x | |||||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 2x | |||||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x | ||||||
| + | 6x |
Pull the next terms from the original dividend down into the current dividend.
| 2x | |||||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x | ||||||
| + | 6x | – | 7 |
Divide the highest order term in the dividend 6x by the highest order term in divisor 2x.
| 2x | + | 3 | |||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x | ||||||
| + | 6x | – | 7 |
Multiply the new quotient term by the divisor.
| 2x | + | 3 | |||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x | ||||||
| + | 6x | – | 7 | ||||||
| + | 6x | – | 9 |
The expression needs to be subtracted from the dividend, so change all the signs in 6x-9
| 2x | + | 3 | |||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x | ||||||
| + | 6x | – | 7 | ||||||
| – | 6x | + | 9 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 2x | + | 3 | |||||||
| 2x | – | 3 | 4×2 | + | 0x | – | 7 | ||
| – | 4×2 | + | 6x | ||||||
| + | 6x | – | 7 | ||||||
| – | 6x | + | 9 | ||||||
| + | 2 |
The final answer is the quotient plus the remainder over the divisor.
2x+3+22x-3
Divide (4x^2-7)/(2x-3)
