18x^2-25x-10 divided by 9x+1
It's long division of polynomials
Long division is equivalent to writing down an equation and solving it as follows:
18x^2-25x-10 = (9x+1)(ax + b) + c --->
18x^2-25x-10 = 9ax^2 + (9b+a)x + b + c
9 a = 18 --->
a = 2
9b+a = -25 ---->
b = 3
b + c = -10 --->
c = -13
whew! You're on a roll with the math! :)
oh, and Count, please note my responce on "this is NOT homework". Thank you. :)Write back if you can!
To perform polynomial long division, follow these steps:
1. Arrange the dividend (18x^2 - 25x - 10) and the divisor (9x + 1) in long division format, with the dividend being divided by the divisor.
_______________________
9x + 1 | 18x^2 - 25x - 10
2. Divide the first term of the dividend (18x^2) by the first term of the divisor (9x). Place the result (2x) above the division symbol, and write it down.
2x
______________
9x + 1 | 18x^2 - 25x - 10
3. Multiply the divisor (9x + 1) by the result (2x). Write the product (18x^2 + 2x) below the dividend, aligning like terms.
2x
_______________________
9x + 1 | 18x^2 - 25x - 10
- (18x^2 + 2x)
- 27x - 10
4. Subtract the product (18x^2 + 2x) from the first two terms of the dividend (18x^2 - 25x). Write this result (-27x - 10) below the product.
2x
_______________________
9x + 1 | 18x^2 - 25x - 10
- (18x^2 + 2x)
_______________
- 27x - 10
5. Bring down the remaining term (-10) from the dividend.
2x
_______________________
9x + 1 | 18x^2 - 25x - 10
- (18x^2 + 2x)
_______________
- 27x - 10
- 27x - 3
6. Divide the new term (-27x) by the first term of the divisor (9x). Place the result (-3) above the division symbol, and write it down.
2x - 3
_______________________
9x + 1 | 18x^2 - 25x - 10
- (18x^2 + 2x)
_______________
- 27x - 10
- 27x - 3
7. Multiply the divisor (9x + 1) by the result (-3). Write the product (-27x - 3) below the remaining terms of the dividend.
2x - 3
_______________________
9x + 1 | 18x^2 - 25x - 10
- (18x^2 + 2x)
_______________
- 27x - 10
- 27x - 3
- (-27x - 3)
0
8. Subtract the product (-27x - 3) from the remaining terms of the dividend (-27x - 10).
2x - 3
________________________
9x + 1 | 18x^2 - 25x - 10
- (18x^2 + 2x)
_______________
- 27x - 10
- 27x - 3
- (-27x - 3)
__________
0
9. Since the resulting subtraction is 0, there is no remainder.
10. The final result of the division is the quotient: 2x - 3.
Therefore, the given polynomial, 18x^2 - 25x - 10, divided by 9x + 1, yields a quotient of 2x - 3 with no remainder.