1. The problem is to factor the quadratic expression $d^2 + 2d - 48$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. 3. To factor, we look for two numbers that multiply to $c = -48$ and add to $b = 2$. 4. The pairs of factors of $-48$ are $(6, -8)$, $(-6, 8)$, $(12, -4)$, $(-12, 4)$, etc. 5. Among these, $6 + (-8) = -2$ and $-6 + 8 = 2$. 6. Since we want the sum to be $+2$, the correct pair is $-6$ and $8$. 7. Therefore, the factorization is $(d - 6)(d + 8)$. 8. To verify, expand: $(d - 6)(d + 8) = d^2 + 8d - 6d - 48 = d^2 + 2d - 48$. 9. Hence, the correct factorization is $(d - 6)(d + 8)$.