Question

Write the polynomial as the product of linear factors.

f(x) = x^2 + 64

A) f(x) = (x + 8)(x - 8)
B) f(x) = (x + 64)(x - 64)
C) f(x) = (x + 4i)(x - 4i)
D) f(x) = (x + 8i)(x - 8i)

Answer 1

The polynomial f(x) = x^2 + 64 can be written as the product of linear factors (x + 8i)(x - 8i).

Step-by-step explanation:

The polynomial f(x) = x^2 + 64 can be written as the product of linear factors using the difference of squares formula.

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

In this case, the expression x^2 + 64 can be viewed as x^2 - (-64) since -64 can be written as -1 * 8^2. Therefore, we can write x^2 + 64 as (x + 8i)(x - 8i).