Which polynomial is prime?

A polynomial is prime if it cannot be factored into polynomials with integer coefficients. The first three choices factor: x² − 25 = (x − 5)(x + 5), 3x² − 27 = 3(x − 3)(x + 3), and 2x² − 8 = 2(x − 2)(x + 2). The expression x² + 7 has no such factorization, so x² plus 7 is prime.

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