Directions: Perform the indicated divisions.
The problem:
(8x^3-6x^2+2x)/(4x+1)
This is what i did and what i got:
(4x^5)/(5x) =
The answer that i got was:
0.80x^4
It is so wrong it hurts. How in the world did you get
(8x^3-6x^2+2x) is equal to 4x^5 ?
There are no x^5 in the sentence.
Instead of that, factor 2x out of it.
2x(4x^2 -3x -1)=2x(4x+1)(x-1)
Put that over the denominator and it amazingly comes to a solution rapidly.
To divide (8x^3-6x^2+2x) by (4x+1), you need to use long division or synthetic division. Here's the step-by-step process to solve it using long division:
1. Write the dividend (8x^3-6x^2+2x) inside the long division bracket.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
2. Divide the first term of the dividend (8x^3) by the divisor (4x). The result is 2x^2.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
3. Multiply the divisor (4x + 1) by the quotient (2x^2) and write it below the dividend.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
_________________
- 8x^2 + 2x
4. Subtract (8x^2 - 2x^2) from (-6x^2 + 2x). The result is -8x^2 + 2x.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
__________________
- 8x^2 + 2x
5. Bring down the next term from the dividend, which is 2x.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
__________________
- 8x^2 + 2x
+ 2x
6. Divide (- 8x^2 + 2x) by the divisor (4x + 1). The result is -2x.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
__________________
- 8x^2 + 2x
+ 2x
- (- 8x^2 - 2x)
7. Multiply the divisor (4x + 1) by the quotient (-2x) and write it below the previous result.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
__________________
- 8x^2 + 2x
+ 2x
- (- 8x^2 - 2x)
______________
4x
8. Subtract (4x - 4x) from (2x + 2x). The result is 4x.
_______________________________________
| 2x^2 - 3x - 1
4x + 1 | 8x^3 - 6x^2 + 2x
- (8x^3 + 2x^2)
__________________
- 8x^2 + 2x
+ 2x
- (- 8x^2 - 2x)
______________
4x
9. There are no more terms to bring down, so the division is complete. The quotient is 2x^2 - 2x + 4x, which simplifies to 2x^2 + 2x.
Therefore, the correct answer is 2x^2 + 2x. The previous answer of 0.80x^4 was incorrect.