Factorise using the cross method: \( 3 x^{2}-13 x-10 \)

To factorise the quadratic \( 3x^{2} - 13x - 10 \) using the cross method, we start by multiplying the coefficient of \( x^{2} \) (which is 3) with the constant term (which is -10). So, \( 3 \times -10 = -30 \). Next, we need to find two numbers that multiply to -30 and add up to -13. The pair that works here is -15 and 2. Now, we split the middle term using these numbers: \( 3x^{2} - 15x + 2x - 10 \). Now, group them: \( (3x^{2} - 15x) + (2x - 10) \). Factor each group: \( 3x(x - 5) + 2(x - 5) \). Now, we can factor out the common binomial: \( (3x + 2)(x - 5) \). So the factorised form is \( (3x + 2)(x - 5) \). Enjoy solving more quadratics!