A prime polynomial cannot be written as a product of lower-degree polynomials. Which polynomial is prime?

For a quadratic to factor into lower-degree polynomials with rational coefficients, its discriminant must be a perfect square. For choice C, the discriminant is (-6)² − 4(8)(−3) = 132, which is not a perfect square, so the polynomial cannot be factored that way. The other choices have perfect-square discriminants, so 8x² − 6x − 3 is prime.

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