To factor the given polynomial completely, we can recognize it as a quadratic in terms of c2. We will use substitution to simplify the expression, factor it as a quadratic, and then substitute back to get the factors in terms of c.
Step 1: Recognize the Polynomial Structure
The given polynomial is 121c4−44c2+4. We can treat this as a quadratic in terms of c2 by letting x=c2. Thus, we rewrite the polynomial as 121x2−44x+4.
Step 2: Factor the Quadratic
Next, we factor the quadratic expression 121x2−44x+4. The factored form is (11x−2)2. Substituting back x=c2, we have:
(11c2−2)2
Step 3: Write the Complete Factorization
The complete factorization of the original polynomial 121c4−44c2+4 is:
(11c2−2)2
Final Answer
The complete factorization is \\(\boxed{(11 c^{2} - 2)^{2}}\\).