Rewrite a polynomial in factored form to reveal its zeros
Problem
Factor \(x^3~-~4x\) completely and state all real zeros.
Big Picture
What this problem is really about
Complete factoring often happens in layers. Start with the greatest common factor, then inspect what remains for a second recognizable pattern such as a difference of squares. Only after every zero-producing factor is visible should each factor be set equal to zero, which prevents hidden factors from hiding additional real zeros.
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