Which polynomial is prime?

A polynomial is prime if it cannot be factored into lower-degree polynomials with integer coefficients. The discriminant of x² + x + 1 is 1² − 4(1)(1) = −3, so it has no real roots and cannot be factored into linear factors with integer coefficients. The other choices factor: x² − x − 2 = (x − 2)(x + 1), x² − 12x + 11 = (x − 1)(x − 11), and x² + 2x − 8 = (x + 4)(x − 2). Thus, choice A, x² + x + 1, is prime.

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