Final answer:
The quadratic equation x²+8x+15=0 can be factored into (x+3)(x+5)=0. Using the Zero Factor Property, the solutions are x = -3 or x = -5.
Step-by-step explanation:
To solve the quadratic equation x²+8x+15=0 using the Zero Factor Property, we must first factor the equation into the form (x+a)(x+b) = 0, where both a and b are numbers that when multiplied give us the constant term 15, and when added, give us the coefficient of x, which is 8.
Looking at the factors of 15, we notice that 3 and 5 are suitable numbers because 3*5=15 and 3+5=8. Therefore, we can rewrite the equation as (x+3)(x+5)=0.
Applying the Zero Factor Property, we set each factor equal to zero: x + 3 = 0 or x + 5 = 0. Solving for x, we get two possible solutions for the equation: x = -3 or x = -5.