Set 7: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. For $2x^2 + 7 x + 3$, find factors of $2\times 3 = 6$ that add to 7: $1+ 6 = 7$ ✓. Split middle: $2x^2 + x + 6 x + 3$. Group: $x(2 x + 1) + 3(2 x + 1) = (2 x + 1)(x + 3)$. Verify: $(2 x + 1)(x + 3) = 2 x^2 + 6 x + x + 3 = 2 x^2 + 7 x + 3$ ✓. Choice B is incorrect because $(2 x + 3)(x + 1) = 2 x^2 + 5 x + 3$ (wrong middle term). Choice C is incorrect because $(x + 1)(x + 3) = x^2 + 4 x + 3$ (missing coefficient of 2 on $x^2$). Choice D is incorrect because $2(x + 1)(x + 3) = 2 x^2 + 8 x + 6$ (wrong coefficients).