-10x+25×2-85x-1
Reorder -10x and 25×2.
25×2-10x-85x-1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 5x | – | 1 | 25×2 | – | 10x | – | 8 |
Divide the highest order term in the dividend 25×2 by the highest order term in divisor 5x.
| 5x | |||||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 |
Multiply the new quotient term by the divisor.
| 5x | |||||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| + | 25×2 | – | 5x |
The expression needs to be subtracted from the dividend, so change all the signs in 25×2-5x
| 5x | |||||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 5x | |||||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x | ||||||
| – | 5x |
Pull the next terms from the original dividend down into the current dividend.
| 5x | |||||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x | ||||||
| – | 5x | – | 8 |
Divide the highest order term in the dividend -5x by the highest order term in divisor 5x.
| 5x | – | 1 | |||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x | ||||||
| – | 5x | – | 8 |
Multiply the new quotient term by the divisor.
| 5x | – | 1 | |||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x | ||||||
| – | 5x | – | 8 | ||||||
| – | 5x | + | 1 |
The expression needs to be subtracted from the dividend, so change all the signs in -5x+1
| 5x | – | 1 | |||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x | ||||||
| – | 5x | – | 8 | ||||||
| + | 5x | – | 1 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| 5x | – | 1 | |||||||
| 5x | – | 1 | 25×2 | – | 10x | – | 8 | ||
| – | 25×2 | + | 5x | ||||||
| – | 5x | – | 8 | ||||||
| + | 5x | – | 1 | ||||||
| – | 9 |
The final answer is the quotient plus the remainder over the divisor.
5x-1-95x-1
Divide (-10x+25x^2-8)/(5x-1)
