Factor. \( 5 x^{2}-29 x-6 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The trinomial is not factorable. (Factor completely.)

Let's factor the expression \( 5x^2 - 29x - 6 \). To do this, we look for two numbers that multiply to \( 5 \times (-6) = -30 \) and add to \(-29\). The numbers \(-30\) and \(1\) do the trick! We can rewrite the middle term: \[ 5x^2 - 30x + x - 6 \] Grouping gives us: \[ 5x(x - 6) + 1(x - 6) = (5x + 1)(x - 6) \] So, the factored form is \( (5x + 1)(x - 6) \). If you ever find yourself stuck while factoring, remember to check that the first coefficient isn’t just 1; identifying the correct pair of numbers is crucial, and checking the product and sum can save you time! Common mistakes include forgetting the signs or miscalculating the product. Always double-check your pairs before concluding that it's unfactorable!