Fictonse Factonise \( 6 x^{2}-47 x-8 \)

To factor the quadratic \( 6x^{2} - 47x - 8 \), you can look for two numbers that multiply to \( 6 \times -8 = -48 \) and add to \(-47\). These numbers are \(-48\) and \(1\). Rewriting the middle term gives us \( 6x^2 - 48x + x - 8 \). Factor by grouping: \( 6x(x - 8) + 1(x - 8) = (6x + 1)(x - 8) \). Now you have the factored form: \( (6x + 1)(x - 8) \). To ensure your factors are correct, you can always expand them back to check if you regenerate your original expression. It’s a nice practice that helps develop your factoring skills, especially when dealing with more complex polynomials!