Interpret complex polynomial/rational expressions by treating parts as single units.
Assign visible features to equivalent algebraic forms
Problem
Compare \(x^2~-~5x~+~6\) with \((x~-~2)(x~-~3)\). State the features directly visible in each form and their relationship as functions.
Big Picture
What this problem is really about
Equivalent forms are different views of the same function, and each view makes certain features easier to read. Expanded form foregrounds degree, leading coefficient, and the constant that gives the vertical intercept. Factored form foregrounds zeros and their multiplicities; expanding the product is the check that both descriptions belong to one polynomial.
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