Choose the most useful rewrite of an expression for a given question
Problem
Rewrite \(x^2~-~5x~+~6\) in the form most useful for finding its zeros, and explain why that form is useful.
Big Picture
What this problem is really about
The most useful algebraic form depends on the feature being studied. For zeros, a product of factors is efficient because the zero-product property turns one equation into separate factor equations. Expanded form still represents the same polynomial, but its coefficients foreground different information and make the zeros less immediate.
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