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