Plz . which polynomials are prime? check all of the boxes that apply.
x2 + 9
x2 – 9
x2 + 3x + 9
–2x2 + 8

Note that a prime polynomial cannot be factored into polynomials with lower degrees, with real integer coefficients.
Therefore we can test whether the discriminant of a quadratic polynomial to see if it is a perfect square. If the discriminant is not a perfect square, the polynomial is prime.

Note that for the quadratic polynomial ax² + bx + c, the discriminant is
D = b² - 4ac.

Test x² + 9
D = -4*9 = -36
The polynomial is prime.

Test x² - 9
D = 4*9 = 36 (perfect square)
The polynomial is not prime.

Test x² + 3x + 9
D = 9 - 4*9 = -27
The polynomial is prime.

Test -2x² + 8
D = -4(-2)(8) = 64 (perfect square)
The polynomial is not prime.

The prime polynomials are
x² + 9
x² + 3x + 9

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