Final answer:
To complete the square for the expression x² - 8x, add the term 16, resulting in the perfect square (x - 4)².
Step-by-step explanation:
The term that must be added to x² - 8x to complete the square is found by taking half of the coefficient of x, which is -8, and then squaring it. The process is as follows:
- Divide the coefficient of x by 2: -8/2 = -4.
- Square the result: (-4)² = 16.
Therefore, the term that needs to be added to x² - 8x to complete the square is 16. When this term is added, the trinomial becomes a perfect square x² - 8x + 16, which can be factored to (x - 4)².