Let's learn how to factor the expression \(x^2 + 5x + 6\) step by step! 🌟 1. We want to find two numbers that multiply to give the last number, 6, and add up to the middle number, 5. 2. The pairs of numbers that multiply to 6 are: - 1 and 6 (1 × 6 = 6, but 1 + 6 = 7, not 5) - 2 and 3 (2 × 3 = 6, and 2 + 3 = 5! Perfect!) 3. So, we can write the middle term \(5x\) as \(2x + 3x\). 4. Rewrite the expression: \(x^2 + 2x + 3x + 6\). 5. Now, group the terms: \((x^2 + 2x) + (3x + 6)\). 6. Factor each group: - From \(x^2 + 2x\), factor out \(x\): \(x(x + 2)\) - From \(3x + 6\), factor out \(3\): \(3(x + 2)\) 7. Now, both groups have \((x + 2)\), so factor that out: \((x + 2)(x + 3)\). **Final answer:** \(x^2 + 5x + 6 = (x + 2)(x + 3)\) Great job! You just factored a quadratic expression! 🎉 Keep practicing, and it will get easier and more fun.