Final answer:
The trinomial x² + 8x + 15 can be factored into (x + 3)(x + 5) by finding two numbers that multiply to 15 and add to 8. For general quadratic equations, solutions can be found using the quadratic formula.
Step-by-step explanation:
To factor the quadratic trinomial x² + 8x + 15, we are looking for two numbers that multiply to give the constant term (15) and add up to give the linear coefficient (8). These two numbers are 3 and 5, since 3 × 5 = 15 and 3 + 5 = 8. Therefore, the factored form of the trinomial is (x + 3)(x + 5).
When dealing with quadratic equations in general, such as at² + bt + c = 0, we can often use the quadratic formula to find the solutions for t. This formula is t = −b ± √(b² - 4ac) / (2a), where a, b, and c are coefficients from the equation. It's an essential tool for solving quadratics when factoring is not possible or straightforward.