Final answer:
To complete the square of the expression x² - x, half of the coefficient of x is squared and added. The correct number to add is 1/4 to form the perfect square trinomial (x - 1/2)². However, none of the options provided in the question correctly match this answer.
Step-by-step explanation:
To complete the square of the expression x² - x, we must add a number that forms a perfect square trinomial. The process involves taking half of the coefficient of x, which is -1/2, and then squaring that number. The square of -1/2 is ( -1/2 )² = 1/4. Therefore, the number that must be added to the expression x² - x to complete the square is 1/4. However, since only whole numbers are provided in the options, we consider the case without the coefficient of 1 for x. To complete the square, we take half of the coefficient of x (which is -1), square it, and obtain ( -1/2 )² = 1/4. Since we need a whole number that accurately completes the square, we would actually need to add (1/2)² = 1/4. But since none of the provided options are correct, we must acknowledge an error and unfortunately, none of the options A) 0, B) 1, C) 4, or D) -1 is correct.