A prime polynomial is simply an irreducible polynomial.
[tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial
First, we test the options.
[tex]\mathbf{x + 9y^2}[/tex]
The above function cannot be reduced further.
Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial
[tex]\mathbf{3m + 9n}[/tex]
Factor out 3
[tex]\mathbf{3(m + 3n)}[/tex]
[tex]\mathbf{3m + 9n}[/tex] is not a prime because it can be factored as [tex]\mathbf{3(m + 3n)}[/tex]
[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex]
Factor out x
[tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]
[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex] is not a prime because it can be factored as [tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]
Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial
Read more about prime polynomials at:
https://brainly.com/question/15562251
