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M2-011-A13-V04
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A-SSE.3.a
Warmup
M2-011-A13-V04
Factor quadratics to reveal zeros of the function they define.
Interpret factors in an area expression
Problem
Using the rectangle diagram and \(A=(3x-2)(x+4)\), label both dimensions and the area units. Solve the two positivity conditions, identify the stricter domain restriction, and interpret each factor’s zero as a boundary.
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A
The side lengths are 3x − 2 and x + 4, but only x + 4 needs to be positive. Both physical lengths must be positive.
B
Negative or zero side lengths are valid rectangles, so both zero values are valid dimensions. A positive-area rectangle requires both lengths to be positive.
C
The side lengths are 3x − 2 and x + 4 units, so the area is in square units. Both must be positive, requiring x > 2/3; 2/3 and −4 are algebraic zero boundaries, with 2/3 degenerate.
D
The factors are square-unit areas, so their product has fourth-power units and x may be any real number. The factors represent lengths, not separate areas.
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Curriculum context
Standard A-SSE.3.a
Category Algebra
Domain Seeing Structure in Expressions
Objective Factor quadratics to reveal zeros of the function they define.
Problem type Interpret factors in an area expression
