(5×2+14x+3)÷(x+2)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| x | + | 2 | 5×2 | + | 14x | + | 3 |
Divide the highest order term in the dividend 5×2 by the highest order term in divisor x.
| 5x | |||||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 |
Multiply the new quotient term by the divisor.
| 5x | |||||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| + | 5×2 | + | 10x |
The expression needs to be subtracted from the dividend, so change all the signs in 5×2+10x
| 5x | |||||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 5x | |||||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x | ||||||
| + | 4x |
Pull the next terms from the original dividend down into the current dividend.
| 5x | |||||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x | ||||||
| + | 4x | + | 3 |
Divide the highest order term in the dividend 4x by the highest order term in divisor x.
| 5x | + | 4 | |||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x | ||||||
| + | 4x | + | 3 |
Multiply the new quotient term by the divisor.
| 5x | + | 4 | |||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x | ||||||
| + | 4x | + | 3 | ||||||
| + | 4x | + | 8 |
The expression needs to be subtracted from the dividend, so change all the signs in 4x+8
| 5x | + | 4 | |||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x | ||||||
| + | 4x | + | 3 | ||||||
| – | 4x | – | 8 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 5x | + | 4 | |||||||
| x | + | 2 | 5×2 | + | 14x | + | 3 | ||
| – | 5×2 | – | 10x | ||||||
| + | 4x | + | 3 | ||||||
| – | 4x | – | 8 | ||||||
| – | 5 |
The final answer is the quotient plus the remainder over the divisor.
5x+4-5x+2
Divide (5x^2+14x+3)÷(x+2)
