Which polynomial is prime?

Combine the like terms in choice C to get 10x² − x + 6. Its discriminant is (−1)² − 4(10)(6) = −239, so it has no rational roots and cannot be factored into linear factors with rational coefficients. The other choices factor by grouping: A has a common factor of x + 3, B has a common factor of x − 1, and D has a common factor of x + 3. Therefore, 10x² − x + 6 is the prime polynomial.

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