\( 1<\quad \begin{array}{l}\text { Find the GCF } \\ 5 x^{5}, 5 x,-30\end{array} \)

To find the GCF (Greatest Common Factor) of the expressions \(5x^5\), \(5x\), and \(-30\), we first identify the factors of each term. The numbers involved are 5 and 30. The prime factorization of 30 is \(2 \times 3 \times 5\), and both \(5x^5\) and \(5x\) share the factor of 5. Therefore, the GCF in terms of numerical values is 5. For the variable \(x\), the lowest power present is \(x^1\) from \(5x\). Hence, the overall GCF is \(5x\). Not only does finding the GCF help simplify expressions, but it’s also essential in factoring polynomials and solving equations. By extracting maximum common factors, you can reduce complex problems to simpler ones, making calculations much more manageable. This skill becomes particularly handy in algebra and higher-level math! In real-world scenarios, knowing how to calculate the GCF can help optimize solutions in various fields, such as engineering and economics. For instance, when trying to align production ratios in manufacturing, finding the GCF of production quantities can help determine the minimum viable batch size that satisfies all constraints. Such practical applications highlight the importance of this fundamental mathematical concept!