Set 5: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. To factor the quadratic trinomial $x^2 + 7 x + 12$, we look for two numbers that multiply to the constant term (12) and add up to the coefficient of the linear term (7). 1. List factors of 12: (1, 12), (2, 6), (3, 4). 2. Check sums: $1 +12=13$, $2 +6=8$, $3 +4=7$. 3. The correct pair is 3 and 4. Thus, the expression factors to $(x + 3)(x + 4)$. This is a fundamental skill for solving quadratic equations and analyzing parabolic graphs. Choice B is incorrect because although $2\times 6 = 12$, their sum is $2 +6=8$, not 7. Choice C is incorrect because $(x-3)(x-4)$ expands to $x^2 - 7 x + 12$, where the middle term is negative. Choice D is incorrect because $1 +12=13$, which does not match the middle term of 7.