Factor out the greatest common factor in

To factor out the greatest common factor (GCF) in the expression , we first identify the GCF of the coefficients 12 and 18, which is 6. Additionally, both terms contain at least one x, so the GCF in terms of the variable is . Thus, the GCF of the entire expression is .

Now, we can factor this out:

So, the factored form of is .

Now, if you’re trying to understand why factoring is so useful, think of it like simplifying your life! Just as getting rid of clutter makes it easier to find what you need, factoring makes equations simpler to solve or analyze. It can also reveal hidden patterns in algebra that can help in problem-solving.

When factoring, the common mistake is forgetting to consider all factors. Always check if you can factor even further or if you missed a common factor. It’s easy to overlook a small number or variable, so double-checking can save you from frustration later!