(6) \( x^{2}+5 x-6 \)

To factor the quadratic expression \( x^2 + 5x - 6 \), you can look for two numbers that multiply to -6 (the constant term) and add to +5 (the coefficient of the linear term). Those numbers are +6 and -1. So the factored form is \( (x + 6)(x - 1) \), which easily gives you the roots \( x = -6 \) and \( x = 1 \) when set to zero. If you're solving real-life problems, this kind of quadratic equation can emerge in various scenarios such as optimizing area or profit. For instance, if you had a rectangular garden and you knew that its dimensions are related to this equation, factoring it can help you easily find the possible lengths and widths that will yield the desired area. It's always a good idea to remember that quadratic equations show up everywhere in everyday calculations, from nature to business!