Factor \( x^{4}+2 x^{2}+1 \) completely. All factors in your answer should have integer coefficients. Submit

The expression \( x^{4}+2 x^{2}+1 \) can be factored by recognizing it as a perfect square trinomial. Specifically, it can be rewritten as: \[ (x^{2}+1)^{2} \] This means that the complete factorization of \( x^{4}+2 x^{2}+1 \) is: \[ (x^{2}+1)(x^{2}+1) \quad \text{or} \quad (x^{2}+1)^{2} \] Hence, the factors are \( (x^2 + 1) \, (x^2 + 1) \) or just \( (x^2 + 1)^2 \).