2. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.058. Perform the division. (Simplify your answer completely.) Divide \( z^{2}+16 z+72 \) by \( z+8 \). \( \square \) SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.073.

To divide \( z^{2}+16z+72 \) by \( z+8 \), you can use polynomial long division or synthetic division. When using long division, you first determine how many times \( z \) from the divisor \( z+8 \) fits into the leading term of the dividend \( z^2 \). This gives you \( z \). Multiply \( z \) by the entire divisor, subtract, and continue until you've completed the division. The result will be \( z + 8 \) with a remainder of \( 0 \), simplifying to \( z + 8 \). In many real-world applications like engineering or physics, understanding polynomial division is crucial for solving equations that model various phenomena. For example, breaking down complex systems into manageable parts, you may need to factor polynomials to analyze system behaviors or optimize designs, turning abstract calculations into practical solutions that drive innovation!