Question

Write a linear factorization of the function. f(x) = x^4 + 4x^2

Answer 1

We can factor x^2 from both terms:

$x^2(x^2+4)$

This is a complete factorization over the reals, we can't go any deeper. If you're allowed to use complex numbers, we can continue to factor the parenthesis:

$x^2(x^2+4)=x^2(x+2i)(x-2i)$

Answer 2

The linear factorization of the function f(x) = x⁴ + 4x² is f(x) = x² (x² + 4)

How to determine the linear factorization?

The equation of the function is given as:

f(x) = x⁴ + 4x²

Rewrite the function as:

f(x) = x² * x² + 4 * x²

Factor out x² in the equation

f(x) = x² (x² + 4)

Hence, the linear factorization of the function f(x) = x⁴ + 4x² is f(x) = x² (x² + 4)

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