To determine which polynomial identity results from dividing \(x^3 + a^3\) by \(x + a\), we can use the formula for the sum of cubes, which states:
\[ x^3 + a^3 = (x + a)(x^2 - ax + a^2) \]
Here, \(x^3 + a^3\) is factored into \((x + a)\) times \((x^2 - ax + a^2)\).
When you divide \(x^3 + a^3\) by \(x + a\), the quotient is \(x^2 - ax + a^2\).
Therefore, the correct option is:
Option #2: \(x^2 - ax + a^2\).