Question
Factor \( x^{4}+2 x^{2}+1 \) completely. All factors in your answer should have integer coefficients. Submit
Ask by Luna Simmons. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{4}+2x^{2}+1 = (x^{2}+1)^{2} \)
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Beyond the Answer
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 \( (x^2 + 1)^2 \).
