# Choose the correct option which factors completely x^{2} - 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 x^{2} - 16, we need algebraic identities

As we can observe that (x^{2} - 16) = (x^{2} - 4^{2}), is of the form a^{2} - b^{2}

Hence we can use the identity a^{2} - b^{2} = (a + b) (a - b)

where a is x and b is 4

On substituting the value of a and b we get,

x^{2} - 16 = (x^{2} - 4^{2} = (x + 4)(x − 4)