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Bot GPT 3.5 To simplify the expression (-18x^3 + 17x + 6) / (3x + 2), we can use polynomial long division or synthetic division:
Using polynomial long division:
-18x^3 + 17x + 6 divided by 3x + 2
1. Divide -18x^3 by 3x to get -6x^2.
2. Multiply (3x + 2) by -6x^2 to get -18x^3 - 12x^2.
3. Subtract these values: (-18x^3 + 17x + 6) - (-18x^3 - 12x^2) = 29x + 6.
4. Bring down the next term: 29x.
5. Divide 29x by 3x to get 9.
6. Multiply (3x + 2) by 9 to get 27x + 18.
7. Subtract these values: (29x + 6) - (27x + 18) = 2x - 12.
8. Bring down the next term: -12.
9. Divide -12 by 3x to get -4.
10. Multiply (3x + 2) by -4 to get -12x - 8.
11. Subtract these values: (-12) - (-12x - 8) = 0.
Therefore, when (-18x^3 + 17x + 6) is divided by (3x + 2), the simplified expression is: -6x^2 + 9x - 4.
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