Questions: Factor completely. 121 c^4 - 44 c^2 + 4

Factor completely.
121 c^4 - 44 c^2 + 4
Transcript text: Factor completely. \[ 121 c^{4}-44 c^{2}+4= \]
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Solution

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Solution Steps

To factor the given polynomial completely, we can recognize it as a quadratic in terms of c2 c^2 . 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 c .

Step 1: Recognize the Polynomial Structure

The given polynomial is 121c444c2+4 121 c^{4} - 44 c^{2} + 4 . We can treat this as a quadratic in terms of c2 c^{2} by letting x=c2 x = c^{2} . Thus, we rewrite the polynomial as 121x244x+4 121 x^{2} - 44 x + 4 .

Step 2: Factor the Quadratic

Next, we factor the quadratic expression 121x244x+4 121 x^{2} - 44 x + 4 . The factored form is (11x2)2 (11 x - 2)^{2} . Substituting back x=c2 x = c^{2} , we have:

(11c22)2 (11 c^{2} - 2)^{2}

Step 3: Write the Complete Factorization

The complete factorization of the original polynomial 121c444c2+4 121 c^{4} - 44 c^{2} + 4 is:

(11c22)2 (11 c^{2} - 2)^{2}

Final Answer

The complete factorization is \\(\boxed{(11 c^{2} - 2)^{2}}\\).

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