Write a linear factorization of the function. f(x) = x⁴ + 9x²

Solution:

Given function f(x) = x⁴ + 9x²

= (x² - 0)(x² + 9)

= x² (x² - (3i)²)

we know that a² - b² = (a + b)(a - b)

= (x - 0)(x - 0)(x + 3i)(x - 3i)

Thus the required factored form is x²(x + 3i)(x - 3i)

Write a linear factorization of the function. f(x) = x⁴ + 9x²

Summary:

The linear factorisation of the function f(x) = x⁴ + 9x² is x²(x + 3i)(x - 3i).