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

Solution Steps

To factor the given polynomial completely, we can recognize it as a quadratic in terms of $c^2$. We will use substitution to simplify the expression, factor it as a quadratic, and then substitute back to get the factors in terms of $c$.

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

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

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

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

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

Final Answer