Problem

Factor \(x^{4}-5x^{2}+4\) completely in \(x\). Substitute one variable for \(x^{2}\), factor the resulting quadratic, restore \(x^{2}\), and continue until every factor is linear.

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substitution=u=x²; expression in u=u²−5u+4; factor in u=(u−1)(u−4); back-substitution=(x²−1)(x²−4); complete factors claimed=(x²−1)(x²−4); expansion=original

substitution=u=x²; expression in u=u²−5x²+4; factorization in u=not possible as written; back-substitution=original; complete factors=none; expansion=original

substitution=u=x²; expression in u=u²−5u+4; factor in u=(u−1)(u−4); back-substitution=(x²−1)(x²−4); completely factored=(x−1)(x+1)(x−2)(x+2); expansion check=original

substitution=u=x²; expression in u=u²−5u+4; factor in u=(u−1)(u−4); back-substitution=omitted; complete factors=(u−1)(u−4); expansion check=not in x

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Factor \(x^{4}-5x^{2}+4\) completely in \(x\). Substitute one variable for \(x^{2}\), factor the resulting quadratic, restore \(x^{2}\), and continue until every factor is linear.

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