6. If \( (x+1)^{2} \) is one of the linear factors of the expression \( \left(x^{2}-1\right)^{2} \), then the othe factor is \( \begin{array}{llll}\text { (a) }(x-1)^{2} & \text { (b) }(x-1) & \text { (c) }\left(x^{2}+1\right) & \text { (d) }\left(x^{2}-1\right)\end{array} \)

To determine the other factor of the expression \((x^2 - 1)^2\) given that \((x + 1)^2\) is one of the linear factors, we can start by factoring \((x^2 - 1)\). We know that: \[ x^2 - 1 = (x - 1)(x + 1) \] Then, squaring that gives us: \[ (x^2 - 1)^2 = ((x - 1)(x + 1))^2 = (x - 1)^2(x + 1)^2 \] Thus, the complete expansion shows that \((x + 1)^2\) is indeed one of the factors. The linear factor associated with \( (x - 1)^2 \) is also present. Therefore, the other factor must be: \[ (x - 1)^2 \] So the answer is (a) \((x - 1)^2\).