Final answer:
The HCF of (x² - 9) and (x² - 16) is (x + 3)(x - 3).
Step-by-step explanation:
To find the HCF of (x² - 9) and (x² - 16), we need to factorize both expressions. The first expression, x² - 9, can be factored as (x + 3)(x - 3) using the difference of squares formula.
The second expression, x² - 16, can be factored as (x + 4)(x - 4) using the difference of squares formula as well.
The HCF is the common factor between the two factorizations, which is (x + 3)(x - 3).