Factoring Trinomial 6Ee727

1. **State the problem:** Factor the trinomial $$x^2 + 25x + 144$$ if possible. 2. **Recall the factoring formula:** For a trinomial of the form $$x^2 + bx + c$$, we look for two numbers that multiply to $$c$$ and add to $$b$$. 3. **Identify values:** Here, $$b = 25$$ and $$c = 144$$. 4. **Find factors of 144 that add to 25:** The pairs of factors of 144 are: - 1 and 144 (sum 145) - 2 and 72 (sum 74) - 3 and 48 (sum 51) - 4 and 36 (sum 40) - 6 and 24 (sum 30) - 8 and 18 (sum 26) - 9 and 16 (sum 25) 5. Since $$9 + 16 = 25$$, these are the numbers we need. 6. **Write the factorization:** $$ x^2 + 25x + 144 = (x + 9)(x + 16) $$ 7. **Check the options:** The options given are: - $$(x - 9)(x + 16)$$ - $$(x - 16)(x - 9)$$ Neither matches the correct factorization $$(x + 9)(x + 16)$$. 8. **Conclusion:** The trinomial factors as $$(x + 9)(x + 16)$$, which is not listed among the options provided. **Final answer:** The correct factorization is $$(x + 9)(x + 16)$$, which is not among the given choices.