Factor \( x^{2}-11 x-60 \) \( \begin{array}{l}(x-10)(x+6) \\ (x-15)(x+4) \\ (x+15)(x-4) \\ (x-12)(x+5)\end{array} \)

To factor the quadratic \( x^{2}-11x-60 \), we need to find two numbers that multiply to \(-60\) (the constant term) and add up to \(-11\) (the coefficient of the \(x\) term). The correct numbers are \(-15\) and \(4\), since \(-15 + 4 = -11\) and \(-15 \times 4 = -60\). Thus, the factorization is \( (x - 15)(x + 4) \). Now, let's take a look at what this means in practice. If you were to graph \( x^{2}-11x-60 \), the x-intercepts (or roots) you find by factoring would be \( x = 15 \) and \( x = -4 \). This helps in understanding how the parabola opens, and where it crosses the x-axis, which can be crucial for solving inequalities or optimization problems related to this function!