1. The problem is to factor the quadratic expression $g^2 + 14g + 24$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=14$, and $c=24$. 3. To factor, we look for two numbers that multiply to $c=24$ and add to $b=14$. 4. The pairs of factors of 24 are: $(1,24)$, $(2,12)$, $(3,8)$, and $(4,6)$. 5. We check which pair sums to 14: - $1 + 24 = 25$ - $2 + 12 = 14$ - $3 + 8 = 11$ - $4 + 6 = 10$ 6. The pair $(2,12)$ sums to 14, so the factorization is: $$g^2 + 14g + 24 = (g + 2)(g + 12)$$ 7. This matches the option $(g + 2)(g + 12)$. Final answer: $(g + 2)(g + 12)$