Solve the quadratic equation: x² - 5x + 6 = 0.

## The reasoning This is a **factorization problem**. We need two numbers that **multiply to give +6** (the constant term) and **add up to give -5** (the coefficient of x). Think: What two numbers multiply to 6? Could be 1×6 or 2×3. Now which pair adds to -5? That's **-2 and -3** (because -2 + -3 = -5, and -2 × -3 = +6). So we rewrite: x² - 5x + 6 = (x - 2)(x - 3) = 0 For this to equal zero, either: - x - 2 = 0 → **x = 2**, OR - x - 3 = 0 → **x = 3** ## Why the wrong options tempt you **Option A (1 or 6):** These multiply to 6, but they add to 7, not -5. You forgot to check the sum. **Option B (-2 or -3):** You found the factors correctly but forgot the final step! If x - 2 = 0, then x = +2, not -2. **Option D (-1 or -6):** Wrong factor pair entirely—these multiply to 6 but add to -7. ## Quick takeaway **Find two numbers that multiply to c and add to b, then set each bracket equal to zero and solve for x—watch your signs!**