First, you can factor out the greatest common factor (GCF) from the expression . The GCF is , so when you factor it out, you get:

Next, look at the quadratic . To see if it can be factored further, check the discriminant (b² - 4ac). Here, :

Since the discriminant is 0, has a perfect square factor, meaning it can be expressed as:

Putting it all together, the fully factored expression is:

But if you’re looking for further exploration beyond simple factoring, read on!

Factoring polynomials is a skill that can be applied extensively in algebra, calculus, and beyond! Understanding these techniques isn’t just about getting the answer; it also lays the groundwork for solving equations, graphing functions, or even working with optimization problems later on! Plus, it makes you feel like a mathematical wizard when you can simplify expressions elegantly!

For practical applications, polynomial factoring is used in various fields like engineering and physics for simplifying calculations. For example, when analyzing forces in physics or designing structures, simplifying expressions through factoring can lead to more manageable equations, making it easier to identify key variables and relationships. So next time you’re faced with complex calculations, remember the magic of factoring!