The problem asks us to factor the expression $x^2 + 64$ if possible. If it cannot be factored, we should state that the polynomial is prime.

1. Problem Description

The problem asks us to factor the expression $x^2 + 64$ if possible. If it cannot be factored, we should state that the polynomial is prime.

2. Solution Steps

We are asked to factor $x^2 + 64$. This is a sum of squares.

The general form for the difference of squares is $a^2 - b^2 = (a-b)(a+b)$.

However, there is no general factorization for the sum of squares $a^2 + b^2$ using real numbers.

In our case, we have $x^2 + 64$. We can write this as $x^2 + 8^2$. Since it is a sum of squares and not a difference of squares, it cannot be factored using real numbers.

Therefore, $x^2 + 64$ is prime.

3. Final Answer

The polynomial is prime.