Welcome back — been a while! Let's pick up where you left off. Step 1: Identify the quadratic expression. The expression to factorize is $z^2 + 5z + 6$. We need to find two numbers that multiply to the constant term (6) and add up to the coefficient of the middle term (5). Step 2: Find the two numbers. Let the two numbers be $a$ and $b$. We need $a \times b = 6$ and $a + b = 5$. The pairs of factors for 6 are (1, 6), (2, 3), (-1, -6), (-2, -3). Checking their sums: $1 + 6 = 7$ $2 + 3 = 5$ $-1 + (-6) = -7$ $-2 + (-3) = -5$ The numbers that satisfy both conditions are 2 and 3. Step 3: Rewrite the middle term using these numbers. $$z^2 + 5z + 6 = z^2 + 2z + 3z + 6$$ Step 4: Factor by grouping. Group the terms and factor out the common factors. $$z^2 + 2z + 3z + 6 = z(z + 2) + 3(z + 2)$$ Step 5: Factor out the common binomial. $$(z + 2)(z + 3)$$ The factored form of the expression is: $$\boxed{(z + 2)(z + 3)} $$ Send me the next one 📸