This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 × 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: (z + 2)(z + 3) Send me the next one 📸