Which polynomials are prime? Check all of the boxes that apply.

A polynomial is prime if it cannot be factored into lower-degree polynomials with integer coefficients. For x² + 9, there are no integer roots, and for x² + 3x + 9 the discriminant is 3² − 4(1)(9) = −27, so it has no rational roots; both are prime. The other choices factor: x² − 9 = (x − 3)(x + 3), and −2x² + 8 = −2(x − 2)(x + 2).

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