24) \( 24 a^{2}-30 a+9 \)

To factor the expression \( 24a^{2}-30a+9 \), you can start by looking for the greatest common factor (GCF) for the coefficients. Here, the GCF is 3. So, extracting that gives \( 3(8a^{2}-10a+3) \). Now for the quadratic \( 8a^{2}-10a+3 \), we look for two numbers that multiply to \( 8 \times 3 = 24 \) and add to \( -10 \). Those numbers are -6 and -4. This allows you to break down the middle term: \( 3(8a^{2}-6a-4a+3) \) which groups to \( 3(2a(4a-3)-1(4a-3)) \), giving you \( 3(4a-3)(2a-1) \). So, the factorization is \( 3(4a-3)(2a-1) \). If you have a problem similar to factorizing, try checking for GCF or using the AC method for quadratics. Always remember to confirm your factors by multiplying them back to check if you retrieve the original expression!