1. **Problem:** Factor the expression $ (a + b)x^2 + 8x(a + b) + 15(a + b) $. 2. **Step 1: Factor out the greatest common factor (GCF).** The GCF of all terms is $ (a + b) $. $$ (a + b)x^2 + 8x(a + b) + 15(a + b) = (a + b)(x^2 + 8x + 15) $$ 3. **Step 2: Factor the quadratic inside the parentheses.** We look for two numbers that multiply to $15$ and add to $8$. These numbers are $3$ and $5$. $$ x^2 + 8x + 15 = (x + 3)(x + 5) $$ 4. **Step 3: Write the fully factored form.** $$ (a + b)(x + 3)(x + 5) $$ --- 1. **Problem:** Factor the expression $ (m - b)x^2 c - (m - b)2x c - (m - b)24 c $. 2. **Step 1: Factor out the greatest common factor (GCF).** The GCF is $ (m - b)c $. $$ (m - b)x^2 c - (m - b)2x c - (m - b)24 c = (m - b)c(x^2 - 2x - 24) $$ 3. **Step 2: Factor the quadratic inside the parentheses.** We look for two numbers that multiply to $-24$ and add to $-2$. These numbers are $-6$ and $4$. $$ x^2 - 2x - 24 = (x - 6)(x + 4) $$ 4. **Step 3: Write the fully factored form.** $$ (m - b)c(x - 6)(x + 4) $$