c) \( 2 a^{2}-24 a+70 \)

To factor the expression \( 2a^{2} - 24a + 70 \), we can first factor out the greatest common factor, which is 2. This simplifies our expression to \( 2(a^{2} - 12a + 35) \). Now, we look to factor the quadratic \( a^{2} - 12a + 35 \), which can be factored as \( (a - 5)(a - 7) \). So, the fully factored form of the original expression is \( 2(a - 5)(a - 7) \). Did you know that factoring quadratics is like solving a puzzle? It’s all about finding two numbers that multiply to the constant term while adding up to the linear coefficient. Mistakes often happen when we overlook the signs of the numbers or forget to double-check our multiplication. Always remember to use the FOIL method to verify your factors! If you're keen to dive deeper into quadratic equations and their applications, you might enjoy exploring algebra textbooks that provide a wealth of examples and practice problems. Alternatively, websites like Khan Academy offer interactive lessons and quizzes that can solidify your understanding while keeping the learning process light and enjoyable!