Write a linear factorization of the function. f(x) = x⁴ + 64x²

Solution:

Given function f(x) = x⁴ + 64x²

Let us re-write 64x² as (8x)²

f(x) = x⁴ + (8x)²

Now, take x² as common from the terms

⇒ x²(x² + 8²)

⇒ x²(x - 2√2i)(x + 2√2i)

Hence, the factors are x, x, 2√2i and -2√2i.

Write a linear factorization of the function. f(x) = x⁴ + 64x²

Summary:

A linear factorization of the function. f(x) = x⁴ + 64x² are x, x, 2√2i and -2√2i.