Final answer:
To factor the quadratic expression x² - 6x - 72, we find two numbers that multiply to -72 and add to -6. Those numbers are -12 and +6, giving us a factored form of (x - 12)(x + 6), where one of the factors is x - 12.
Step-by-step explanation:
The question requires us to identify one of the factors of the quadratic expression x² - 6x - 72 when it is completely factored. This type of problem is solved generally by factoring by grouping or by finding two numbers that multiply to give the product of the coefficient of x² (which is 1 in this case) and the constant term (-72), while also adding up to the coefficient of x (-6).
To factor x² - 6x - 72, we need to find two numbers that multiply to -72 and add up to -6. Those numbers are -12 and +6. Therefore, the factored form of x² - 6x - 72 is (x - 12)(x + 6), so one of the factors is x - 12.