Answer :
A prime polynomial is a non-constant polynomial that has no factors other than itself and a constant. In other words, it cannot be factored into the product of two non-constant polynomials with integer coefficients. Let's check each polynomial:
1. $x^2+4$: This polynomial is a sum of squares, which cannot be factored over the integers. Therefore, it is prime.
2. $x^2-5x+2$: This polynomial can be factored as $(x-2)(x-3)$, so it is not prime.
3. $x^2+10x-24$: This polynomial can be factored as $(x+12)(x-2)$, so it is not prime.
4. $x^2-x+27$: This polynomial cannot be factored over the integers, so it is prime.
5. $2x^3-4x+5x^2-10$: This polynomial can be factored as $2x(x^2-2)+5(x^2-2)$, so it is not prime.
【Answer】: The prime polynomials are $x^2+4$ and $x^2-x+27$.
1. $x^2+4$: This polynomial is a sum of squares, which cannot be factored over the integers. Therefore, it is prime.
2. $x^2-5x+2$: This polynomial can be factored as $(x-2)(x-3)$, so it is not prime.
3. $x^2+10x-24$: This polynomial can be factored as $(x+12)(x-2)$, so it is not prime.
4. $x^2-x+27$: This polynomial cannot be factored over the integers, so it is prime.
5. $2x^3-4x+5x^2-10$: This polynomial can be factored as $2x(x^2-2)+5(x^2-2)$, so it is not prime.
【Answer】: The prime polynomials are $x^2+4$ and $x^2-x+27$.