Final answer:
The solution set for the inequality x² + 2x - 15 > 0 is (-∞, -5) ∪ (3, ∞), meaning the expression is greater than zero when x is less than -5 or greater than 3.
Step-by-step explanation:
The student is attempting to solve an inequality, specifically x² + 2x - 15 > 0. To solve this, we can factor the quadratic equation to find its roots (the values of x where the inequality equals zero). The factored form of the quadratic equation is (x + 5)(x - 3) = 0, where the roots are x = -5 and x = 3. Since the inequality is looking for where the expression is greater than zero, we are interested in the intervals between these roots.
To determine the solution set for the inequality, we can create a sign chart or simply analyze the factors. It's clear that the expression is positive when x is less than -5 or greater than 3. Thus, the solution set for the inequality x² + 2x - 15 > 0 is (-∞, -5) ∪ (3, ∞), where ∞ represents infinity.