Answer:<span>1)
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Quotient: 2x⁵ + x⁴ + (1/3)x³ -(28/9)x² + (91/27)x – (361/81)</span>
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Remainder: 523/81</span>
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2) Since the division is not exact (remainder 523/81) the factor 3x + 1 (the divisor) is not a factor.Explanation (Long division):1)
6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2 | 3x + 1
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2x⁵
2)
</span><span> 6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2 | 3x + 1
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-6x⁶ - 2x⁵ 2x⁵
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3x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2
3)
</span><span> 6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2 | 3x + 1
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-6x⁶ - 2x⁵ 2x⁵ + x⁴
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3x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2
</span>4) <span>
6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2 | 3x + 1
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-6x⁶ - 2x⁵ 2x⁵ + x⁴
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3x⁵ + 2x⁴ - 9x³ + 7x² - 10x + 2
- 3x⁵ - x⁴
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2x⁴ - 9x³ + 7x² - 10x + 2
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</span><span>Since the number of characters to show here is limited, I continue with this division is a separate file.
Please, open the attached pdf file. There you have the entire division.
Remember that if 3x + 1 were a factor the division would be exact. So, since the division is not exact 3x + 1 is not a factor.
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