Answer:
(1/3)x^2 + 5 - 25/(3x^3 - 17x^2 + 15x - 25).
Explanation:
To divide (x - 5) by (3x^3 - 17x^2 + 15x - 25), we can use polynomial long division.
First, let's set up the division:
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3x^3 - 17x^2 + 15x - 25 | x - 5
To start the division, we divide the highest degree term of the dividend (x) by the highest degree term of the divisor (3x^3). This gives us (1/3)x^2, which becomes the first term of the quotient.
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3x^3 - 17x^2 + 15x - 25 | x - 5
- (1/3)x^2
Next, we multiply the divisor (3x^3 - 17x^2 + 15x - 25) by the first term of the quotient (- (1/3)x^2) and subtract it from the dividend (x - 5):
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3x^3 - 17x^2 + 15x - 25 | x - 5
- (1/3)x^2
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0x^3 + (1/3)x^2 + 15x - 25
Now, we bring down the next term from the dividend, which is 15x:
________________
3x^3 - 17x^2 + 15x - 25 | x - 5
- (1/3)x^2
_________________________
0x^3 + (1/3)x^2 + 15x - 25
- 15x
We divide the new dividend (15x) by the highest degree term of the divisor (3x^3), which gives us (5/3). This becomes the next term of the quotient:
________________
3x^3 - 17x^2 + 15x - 25 | x - 5
- (1/3)x^2
_________________________
0x^3 + (1/3)x^2 + 15x - 25
- 15x
__________________
0x^2 - 25
Finally, we bring down the last term from the dividend, which is -25:
________________
3x^3 - 17x^2 + 15x - 25 | x - 5
- (1/3)x^2
_________________________
0x^3 + (1/3)x^2 + 15x - 25
- 15x
__________________
0x^2 - 25
- (-25)
Since there are no more terms in the dividend, the division is complete. The quotient is (1/3)x^2 + 5 - 25/(3x^3 - 17x^2 + 15x - 25).
Therefore, (x - 5) divided by (3x^3 - 17x^2 + 15x - 25) is equal to