Problem

Interpret \(x^{2}-9=(x-3)(x+3)\) for an outer square with a \(3\text{-}by-3\) opening and \(x>3~\text{meters}\). Explain the difference-and-sum factors, find the algebraic zeros, filter them through the physical domain, and compare with the displayed answer diagram.

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The factors are (x − 3)(x + 3). Algebraic zeros are −3 and 3; both are physical frame sizes because each makes the area difference zero.

The difference-of-squares factors are (x − 3)(x + 3). Algebraic zeros are −3 and 3; because x > 3, neither zero is a permitted physical frame size. The factors represent outer-side difference and sum with the opening side.

The factors are (x − 9)(x + 1). Algebraic zeros are −1 and 9; with x > 3, 9 is the only physical frame size.

The factors are (x − 3)(x + 3). The only algebraic zero is 3; with x > 3, 3 is a permitted physical frame size.

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Interpret \(x^{2}-9=(x-3)(x+3)\) for an outer square with a \(3\text{-}by-3\) opening and \(x>3~\text{meters}\). Explain the difference-and-sum factors, find the algebraic zeros, filter them through the physical domain, and compare with the displayed answer diagram.

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