The area of a rectangular yard is given by the polynomial 2x² + 7x + 3 square feet. Which pair of binomials could represent the length and width of the yard?
A(2x + 1) and (x + 3)
B(2x + 3) and (x + 1)
C(2x − 1) and (x − 3)
D2(x + 1)(x + 3)
Explanation
Factor 2x² + 7x + 3. Find two numbers that multiply to (2)(3) = 6 and add to 7: 6 and 1. Split: 2x² + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3). Verify by FOIL: 2x·x + 2x·3 + 1·x + 1·3 = 2x² + 6x + x + 3 = 2x² + 7x + 3 ✓. Choice B gives 2x² + 5x + 3 when expanded.
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