Question

Find the HCF of ( x² - 9 ) and ( x² - 16 ).

a. ( (x + 3)(x - 3) )
b. ( (x + 4)(x - 4) )
c. ( (x + 3)(x + 3) )
d. ( (x - 4)(x + 4) )

Answer 1

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).