Write a linear factorization of the function.
f(x) = x4 + 16x2

f(x) = x^2*(x - 4 i)*(x + 4 i)

Step-by-step explanation:

Given

f(x) = x^4 + 16*x^2

First, take the Greatest Common Factor, as follows

f(x) = x^2*(x^2 + 16)

Then, find the roots of (x^2 + 16), as follows

x^2 + 16 =  0

x^2 = -16

x = sqrt(-16)

x = sqrt(-1*16)

x = sqrt(-1)*sqrt(16)

There are 2 solutions,  x1 = 4 i and x2 = -4 i; both of them imaginary. Then, the roots are (x - 4 i) and (x + 4 i). Replacing in the second equation:

f(x) = x^2*(x - 4 i)*(x + 4 i)

And that is the linear factorization.