Final answer:
To complete the square for the polynomial w² - 18w, take half of -18 (which is -9), square it (to get 81), and add it to the expression to get (w - 9)².
Step-by-step explanation:
To complete the square for the polynomial w² - 18w + _____, we need to find a number that when added to w² - 18w, results in a perfect-square quadratic. The process involves taking half of the coefficient of w, squaring it, and adding it to the expression. In this case, we take half of -18, which is -9, and then square it to get 81.
Therefore, the number that completes the square is 81, making the polynomial w² - 18w + 81 a perfect-square quadratic of (w - 9)².