The remainder when \(x^2 - x - 1\) is divided by \(6x^3 + 2x^2 - 5x + 1\) is the same as the remainder when \(6x^3 + 2x^2 - 5x + 1\) is divided by \(x^2 - x - 1\). We can use polynomial long division to find the remainder. The result of the division is:

6x + 8

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x^2 - x - 1 | 6x^3 + 2x^2 - 5x + 1

- (6x^3 - 6x^2 - 6x)

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8x^2 + x + 1

- (8x^2 - 8x - 8)

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9x + 9

So, the remainder when \(6x^3 + 2x^2 - 5x + 1\) is divided by \(x^2 - x - 1\) is 9x + 9