Answer:
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.
