1. **State the problem:** Factor the trinomial $$h^2 + 3h - 40$$ into the form $$(h + a)(h - b)$$ where $a$ and $b$ are numbers to be found. 2. **Recall the factoring rule:** For a trinomial $$h^2 + ph + q$$, we look for two numbers whose product is $$q$$ and whose sum is $$p$$. 3. **Apply the rule:** Here, $$p = 3$$ and $$q = -40$$. 4. **Find two numbers:** We need two numbers that multiply to $$-40$$ and add to $$3$$. 5. **List factor pairs of 40:** - $$1 \times 40$$ - $$2 \times 20$$ - $$4 \times 10$$ - $$5 \times 8$$ 6. **Check sums with signs:** Since the product is negative, one number is positive and the other negative. - $$5 + (-8) = -3$$ - $$8 + (-5) = 3$$ (this matches our sum) 7. **Write the factors:** The numbers are $$8$$ and $$5$$, with signs adjusted to get sum $$3$$ and product $$-40$$. 8. **Final factorization:** $$ (h + 8)(h - 5) $$ **Answer:** The missing numbers are 8 and 5, so the factorization is $$(h + 8)(h - 5)$$.