Question Factor the expression completely. \[ 24 x^{2}+6 \]

First, let's factor out the greatest common factor (GCF) from the expression \(24x^{2} + 6\). The GCF of 24 and 6 is 6, so we can factor that out: \[ 6(4x^{2} + 1) \] Next, we examine the expression \(4x^{2} + 1\). This is a sum of squares, and it cannot be factored further using real numbers. Therefore, the completely factored form of the expression is: \[ 6(4x^{2} + 1) \] To get even more fun with factoring, did you know that the expression demonstrates the beauty of algebra? Factoring not only simplifies equations but can also reveal hidden relationships. For example, in more complex polynomial equations, recognizing patterns like sums of squares or perfect squares allows mathematicians to solve higher-degree polynomials more efficiently. When you start factoring, a common mistake is forgetting to look for a GCF first! Always check for the largest number or variable that divides each term without leaving a remainder. This can save you time and simplify your work before diving into more complex techniques like grouping or using the quadratic formula.