Asked by Huik
Simplify completely
(8x^3-12x^2+18x-27)/(2x-3)-x^2+4x
(8x^3-12x^2+18x-27)/(2x-3)-x^2+4x
Answers
Answered by
GPT 3.5
First, let's simplify the fraction (8x^3-12x^2+18x-27)/(2x-3):
Using polynomial long division, we divide 8x^3-12x^2+18x-27 by 2x-3:
4x^2 - 1
________________
2x - 3 | 8x^3 - 12x^2 + 18x - 27
- (8x^3 - 12x^2)
________________
0 - 0 + 18x - 27
- (0 - 0 + 18x - 27)
________________
0
Therefore, (8x^3-12x^2+18x-27)/(2x-3) simplifies to 4x^2 - 1.
Now, we can rewrite the expression as (4x^2 - 1) - x^2 + 4x:
Combining like terms, we have 4x^2 - x^2 + 4x - 1:
This simplifies to 3x^2 + 4x - 1.
Therefore, the simplified form of (8x^3-12x^2+18x-27)/(2x-3)-x^2+4x is 3x^2 + 4x - 1.
Using polynomial long division, we divide 8x^3-12x^2+18x-27 by 2x-3:
4x^2 - 1
________________
2x - 3 | 8x^3 - 12x^2 + 18x - 27
- (8x^3 - 12x^2)
________________
0 - 0 + 18x - 27
- (0 - 0 + 18x - 27)
________________
0
Therefore, (8x^3-12x^2+18x-27)/(2x-3) simplifies to 4x^2 - 1.
Now, we can rewrite the expression as (4x^2 - 1) - x^2 + 4x:
Combining like terms, we have 4x^2 - x^2 + 4x - 1:
This simplifies to 3x^2 + 4x - 1.
Therefore, the simplified form of (8x^3-12x^2+18x-27)/(2x-3)-x^2+4x is 3x^2 + 4x - 1.
Answered by
GPT 3.5
Apologies for the mistake in my previous response. Let's redo the simplification.
We have the expression (8x^3-12x^2+18x-27)/(2x-3)-x^2+4x.
First, let's simplify the fraction (8x^3-12x^2+18x-27)/(2x-3) using polynomial long division:
4x^2 + 2x + 8
____________________
2x - 3 | 8x^3 - 12x^2 + 18x - 27
- (8x^3 - 12x^2)
____________________
0 + 30x - 27
- (0 - 6x + 9)
____________________
36x - 36
- (36x - 54)
____________________
18
Therefore, (8x^3-12x^2+18x-27)/(2x-3) simplifies to 4x^2 + 2x + 8.
Now, we can rewrite the expression as (4x^2 + 2x + 8) - x^2 + 4x:
Combining like terms, we have 3x^2 + 6x + 8.
Therefore, the simplified form of (8x^3-12x^2+18x-27)/(2x-3)-x^2+4x is 3x^2 + 6x + 8.
We have the expression (8x^3-12x^2+18x-27)/(2x-3)-x^2+4x.
First, let's simplify the fraction (8x^3-12x^2+18x-27)/(2x-3) using polynomial long division:
4x^2 + 2x + 8
____________________
2x - 3 | 8x^3 - 12x^2 + 18x - 27
- (8x^3 - 12x^2)
____________________
0 + 30x - 27
- (0 - 6x + 9)
____________________
36x - 36
- (36x - 54)
____________________
18
Therefore, (8x^3-12x^2+18x-27)/(2x-3) simplifies to 4x^2 + 2x + 8.
Now, we can rewrite the expression as (4x^2 + 2x + 8) - x^2 + 4x:
Combining like terms, we have 3x^2 + 6x + 8.
Therefore, the simplified form of (8x^3-12x^2+18x-27)/(2x-3)-x^2+4x is 3x^2 + 6x + 8.
Answered by
GPT 3.5
Apologies for the confusion caused by the incorrect first response.
To clarify, let's simplify the expression again:
(8x^3 - 12x^2 + 18x - 27)/(2x - 3) - x^2 + 4x
First, let's simplify the fraction (8x^3 - 12x^2 + 18x - 27)/(2x - 3):
Using polynomial long division or synthetic division, we find that the quotient is 4x^2 - 2x - 9, with a remainder of 0. Therefore, (8x^3 - 12x^2 + 18x - 27)/(2x - 3) simplifies to 4x^2 - 2x - 9.
Now, let's rewrite the expression as 4x^2 - 2x - 9 - x^2 + 4x:
Combining like terms, we have 3x^2 + 2x - 9.
Therefore, the simplified form of (8x^3 - 12x^2 + 18x - 27)/(2x - 3) - x^2 + 4x is 3x^2 + 2x - 9.
To clarify, let's simplify the expression again:
(8x^3 - 12x^2 + 18x - 27)/(2x - 3) - x^2 + 4x
First, let's simplify the fraction (8x^3 - 12x^2 + 18x - 27)/(2x - 3):
Using polynomial long division or synthetic division, we find that the quotient is 4x^2 - 2x - 9, with a remainder of 0. Therefore, (8x^3 - 12x^2 + 18x - 27)/(2x - 3) simplifies to 4x^2 - 2x - 9.
Now, let's rewrite the expression as 4x^2 - 2x - 9 - x^2 + 4x:
Combining like terms, we have 3x^2 + 2x - 9.
Therefore, the simplified form of (8x^3 - 12x^2 + 18x - 27)/(2x - 3) - x^2 + 4x is 3x^2 + 2x - 9.
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