Solve: x² − 5x + 6 = 0.

**The reasoning** This is a **quadratic equation** that we solve by **factorization**. We need two numbers that: - Multiply to give +6 (the constant term) - Add to give −5 (the coefficient of x) Those numbers are −2 and −3 (because −2 × −3 = +6, and −2 + (−3) = −5). So we rewrite: x² − 5x + 6 = (x − 2)(x − 3) = 0 If two things multiply to give zero, at least one must be zero: - Either x − 2 = 0 → **x = 2** - Or x − 3 = 0 → **x = 3** **Why the wrong options tempt you** **Option A (1 or 6):** You might spot that 1 × 6 = 6, but forget to check: does 1 + 6 = 5? Yes, but we need *−5*, so the signs are wrong. **Option B (−2 or −3):** These are the factors themselves! Don't confuse the numbers you used *in* the brackets with the actual solutions. **Option D (−1 or −6):** Sign confusion again—happens when you rush. **Quick takeaway** Always verify: plug your answers back in. If x = 2: (2)² − 5(2) + 6 = 4 − 10 + 6 = 0 ✓. Your factors aren't your answers—solve each bracket separately!