Which polynomial is prime?

A polynomial is prime here if it cannot be factored into polynomials with integer coefficients. The expressions in A, C, and D factor as (x − 6)(x + 6), (x − 3)(x − 4), and (x − 5)(x + 4), respectively. For B, x² + 6 has no integer factors: its discriminant is 0² − 4(1)(6) = −24, so it has no real roots and cannot factor into linear polynomials. Therefore, x² + 6 is prime.

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