To find the values of \( x \) where the curve \(y = x^3 + 2x^2 - 5x - 6\) crosses the x-axis, we set \( y = 0 \): \(x^3 + 2x^2 - 5x - 6 = 0\) Testing for rational roots, we find that \( x = -1 \) is a root. Factoring the polynomial gives: \(x^3 + 2x^2 - 5x - 6 = (x + 1)(x^2 + x - 6)\) Solving the quadratic \( x^2 + x - 6 = 0 \) using the quadratic formula yields: \(x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot -6}}{2 \cdot 1} = \frac{-1 \pm 5}{2}\) Thus, the solutions are: \(x = -1, \quad x = 2, \quad x = -3\) Therefore, the values of \( x \) where the curve crosses the x-axis are \(x = -1, \quad x = 2, \quad x = -3\).