Which polynomials are prime? Check all of the boxes that apply.
x² + 9, x² - 9, x² + 3x + 9, -2x² + 8

Solution:

A prime polynomial has only two factors 1 and itself. It is a polynomial with integer coefficients that cannot be factored into polynomials of lower degrees.

To find the prime polynomial, we will factorize all the polynomials.

Equation 1: x² + 9 can not be factorized with rational numbers. Therefore, it is a prime polynomial.

Equation 2: x² - 9 can be factored into (x - 3)(x + 3). Therefore, it is NOT a prime polynomial.

Equation 3: x² + 3x + 9 can not be factorized with rational numbers. Therefore, it is a prime polynomial.

Equation 4: -2x² + 8 can be factored into -2(x - 2)(x + 2). Therefore, it is NOT a prime polynomial.

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

Summary:

The prime polynomial that cannot be factored into a polynomial of lower degree is x² + 9 and x² + 3x + 9.