Which polynomial is prime?

A polynomial is prime if it cannot be factored into lower-degree polynomials with integer coefficients. The expression x² + 7 has no integer roots and does not factor over the integers, so it is prime. The other choices factor: x² − 25 = (x − 5)(x + 5), 3x² − 27 = 3(x − 3)(x + 3), and 2x² − 8 = 2(x − 2)(x + 2).

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