(7×3-8×2-13x+2)÷(7x-1)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 |
Divide the highest order term in the dividend 7×3 by the highest order term in divisor 7x.
| x2 | |||||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 |
Multiply the new quotient term by the divisor.
| x2 | |||||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| + | 7×3 | – | x2 |
The expression needs to be subtracted from the dividend, so change all the signs in 7×3-x2
| x2 | |||||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| x2 | |||||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 |
Pull the next terms from the original dividend down into the current dividend.
| x2 | |||||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x |
Divide the highest order term in the dividend -7×2 by the highest order term in divisor 7x.
| x2 | – | x | |||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x |
Multiply the new quotient term by the divisor.
| x2 | – | x | |||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| – | 7×2 | + | x |
The expression needs to be subtracted from the dividend, so change all the signs in -7×2+x
| x2 | – | x | |||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| x2 | – | x | |||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x | ||||||||
| – | 14x |
Pull the next terms from the original dividend down into the current dividend.
| x2 | – | x | |||||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x | ||||||||
| – | 14x | + | 2 |
Divide the highest order term in the dividend -14x by the highest order term in divisor 7x.
| x2 | – | x | – | 2 | |||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x | ||||||||
| – | 14x | + | 2 |
Multiply the new quotient term by the divisor.
| x2 | – | x | – | 2 | |||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x | ||||||||
| – | 14x | + | 2 | ||||||||
| – | 14x | + | 2 |
The expression needs to be subtracted from the dividend, so change all the signs in -14x+2
| x2 | – | x | – | 2 | |||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x | ||||||||
| – | 14x | + | 2 | ||||||||
| + | 14x | – | 2 |
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
| x2 | – | x | – | 2 | |||||||
| 7x | – | 1 | 7×3 | – | 8×2 | – | 13x | + | 2 | ||
| – | 7×3 | + | x2 | ||||||||
| – | 7×2 | – | 13x | ||||||||
| + | 7×2 | – | x | ||||||||
| – | 14x | + | 2 | ||||||||
| + | 14x | – | 2 | ||||||||
| 0 |
Since the remander is 0, the final answer is the quotient.
x2-x-2
Divide (7x^3-8x^2-13x+2)÷(7x-1)
