To factor the function f(x) = x^4 – 16x^2, we can start by recognizing that this expression is a polynomial. The first step is to factor out the common term.
Notice that we can factor out x^2 from the expression:
f(x) = x^2(x^2 – 16)
The term (x^2 – 16) is a difference of squares, which can be factored further:
x^2 – 16 = (x – 4)(x + 4)
So, substituting this back into our expression gives:
f(x) = x^2(x – 4)(x + 4)
This is the factorization into linear factors.
Therefore, the complete linear factorization of the function f(x) = x^4 – 16x^2 is:
f(x) = x^2(x – 4)(x + 4)
The final answer consists of one quadratic factor, x^2, and two linear factors, (x – 4) and (x + 4).