Factor Trinomial Fcee45

1. **State the problem:** Factor the trinomial $$x^2 + 4x - 5$$ into two binomials. 2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. Here, $$a = 1$$, $$b = 4$$, and $$c = -5$$. 4. Calculate the product $$a \times c = 1 \times (-5) = -5$$. 5. Find two numbers that multiply to $$-5$$ and add to $$4$$. These numbers are $$5$$ and $$-1$$ because $$5 \times (-1) = -5$$ and $$5 + (-1) = 4$$. 6. Rewrite the middle term using these numbers: $$x^2 + 5x - 1x - 5$$. 7. Group terms: $$(x^2 + 5x) + (-1x - 5)$$. 8. Factor each group: $$x(x + 5) - 1(x + 5)$$. 9. Factor out the common binomial: $$(x - 1)(x + 5)$$. 10. **Final answer:** The factorization of $$x^2 + 4x - 5$$ is $$(x-1)(x+5)$$.