Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Choose the most useful equivalent form
Problem
Rewrite \(x^{2}-5x+6\) in the equivalent form that displays its zeros most directly. Name the form, identify both zeros from it, and explain why the expanded and vertex forms are less direct for this task.
Big Picture
What this problem is really about
Equivalent forms emphasize different features, so the requested feature should drive the rewrite. We’ll compare what standard, vertex, and factored forms display directly, identify the representation that exposes zeros with the least extra work, verify the rewrite algebraically, and then read every zero from the resulting structure.
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