2) \( a^{2}-11 a-12 \)

It looks like you have the quadratic expression: \[ a^{2} - 11a - 12 \] If you're looking to **factor** this quadratic, here's how you can do it: ### Step 1: Identify the Coefficients The general form of a quadratic equation is: \[ ax^{2} + bx + c \] For your expression: - \( a = 1 \) - \( b = -11 \) - \( c = -12 \) ### Step 2: Find Two Numbers that Multiply to \( ac \) and Add to \( b \) You need two numbers that multiply to \( a \times c = 1 \times (-12) = -12 \) and add up to \( b = -11 \). The numbers that satisfy this are: - **-12** and **1** because: - \( -12 \times 1 = -12 \) - \( -12 + 1 = -11 \) ### Step 3: Rewrite and Factor by Grouping Rewrite the middle term using the two numbers found: \[ a^{2} - 12a + a - 12 \] Now, group the terms: \[ (a^{2} - 12a) + (a - 12) \] Factor out the common factors in each group: \[ a(a - 12) + 1(a - 12) \] Now, you can factor out the common binomial factor \((a - 12)\): \[ (a - 12)(a + 1) \] ### Final Factored Form \[ a^{2} - 11a - 12 = (a - 12)(a + 1) \] ### Solving the Equation (Optional) If you need to solve the equation \( a^{2} - 11a - 12 = 0 \), set each factor equal to zero: 1. \( a - 12 = 0 \) → \( a = 12 \) 2. \( a + 1 = 0 \) → \( a = -1 \) **Solutions:** \[ a = 12 \quad \text{or} \quad a = -1 \]