6. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.082. Perform the division. (Simplify your answer completely.) \[ \frac{a^{3}+a}{a+2} \]

To perform the division of \( \frac{a^{3}+a}{a+2} \), start by factoring the numerator. Notice that \( a^{3}+a = a(a^{2}+1) \). Now, rewrite the expression as \( \frac{a(a^{2}+1)}{a+2} \). Since \( a+2 \) does not factor into \( a(a^{2}+1) \), we cannot simplify further. The final answer is: \[ \frac{a(a^{2}+1)}{a+2} \] --- Dividing polynomials can sometimes feel daunting, but breaking the problem down is key! Always look for common factors and try to factor polynomials when possible—it can make the problem easier to manage and possibly lead to cancellation. Another handy tip is to remember that synthetic or long division can also be useful for polynomial division. If you find factoring isn't working, these methods can help you tackle the division with more straightforward calculations. Keep practicing, and it will get easier!