1. State the problem: Factor the quadratic $x^2+5x+6$. 2. Use the factoring rule: find two numbers $a$ and $b$ such that $ab=6$ and $a+b=5$. 3. List factor pairs of $6$: - $1\cdot 6=6$ and $1+6=7$ (not $5$) - $2\cdot 3=6$ and $2+3=5$ (works) 4. Rewrite using those numbers: $$x^2+5x+6 = x^2+2x+3x+6$$ 5. Factor by grouping: $$x^2+2x+3x+6 = x(x+2)+3(x+2)$$ 6. Factor out the common binomial: $$x(x+2)+3(x+2) = (x+2)(x+3)$$ 7. Final answer: The factorization is $(x+2)(x+3)$.