Set 12: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. We need to factor the trinomial into $(x + m)(x + n)$ where $mn = 20$ and $m+n = -9$. 1. Since the product is positive and the sum is negative, both numbers must be negative. 2. Pairs of factors for 20: (-1, -20), (-2, -10), (-4, -5). 3. Sums: $-1-20=-21$, $-2-10=-12$, $-4-5=-9$. The correct pair is -4 and -5, so the factorization is $(x - 4)(x - 5)$. Choice B is incorrect because the sum would be +9. Choice C is incorrect because the sum would be -12. Choice D is incorrect because the sum would be +21.