Set 8: Quadratic Equations (Intermediate)

Choice A is correct. Choice A is the correct answer. The area of a rectangle is $\text{Area} = \text{Length} \times \text{Width}$. 1. We are given Area $= x^2 + 5 x + 6$ and Width $= (x + 2)$. 2. We need to find the other factor of the quadratic. 3. Factor $x^2 + 5 x + 6$: We need numbers that multiply to 6 and add to 5. They are 2 and 3. 4. So, $x^2 + 5 x + 6 = (x + 2)(x + 3)$. Since the width is $(x + 2)$, the length must be $(x + 3)$. Choice B is incorrect because $(x+2)(x+4) = x^2 + 6 x + 8$. Choice C is incorrect because $(x+2)(x+2) = x^2 + 4 x + 4$. Choice D is incorrect because $(x+2)(x+1) = x^2 + 3 x + 2$.