Choose the correct option which factors completely x² - 16.

(a) (x + 4)(x + 4)

(b) (x + 4)(x − 4)

(c) prime

(d) (x − 4)(x − 4)

A factor is defined as the number that divides the given number without leaving any remainder. For example, 2 is a factor of 8 since 8 divided by 2 does not leave any remainder.

Answer: Option (b) (x + 4)(x − 4) is the correct answer.

Let us proceed step by step.

Explanation:

To factor x² - 16, we need algebraic identities

As we can observe that (x² - 16) = (x² - 4²), is of the form a² - b²

Hence we can use the identity a² - b² = (a + b) (a - b)

where a is x and b is 4 

On substituting the value of a and b we get,

x² - 16 = (x² - 4² = (x + 4)(x − 4)

Therefore, option (b) (x + 4)(x − 4) is the correct answer as x² - 16 = (x + 4)(x − 4)