Factoring is a popular way to solve quadratic equations, especially for 10th graders. Here are some reasons why students often choose factoring over the quadratic formula:

1. It's Simpler:

   • Factoring is usually quicker. When a quadratic equation can be easily factored, students can skip the tougher calculations that come with the quadratic formula. The quadratic formula looks like this:
     $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
     This formula needs extra steps, like figuring out the discriminant, which is $b^2 - 4ac$.

2. Better Understanding:

   • Factoring helps students really grasp how polynomials work and how to find their roots. Research shows that students who practice factoring can improve their understanding of quadratics by about 30% compared to those who mostly use the quadratic formula.

3. Saves Time:

   • Factoring can be much faster for simpler equations. Studies show that around 70% of students can solve a quadratic by factoring in less than 2 minutes. In contrast, it takes about 4 minutes on average to solve the same problem using the quadratic formula.

4. Boosts Mental Math Skills:

   • Factoring helps students strengthen their mental math. It allows them to think about how to combine products and sums, which helps their overall math skills.

In short, both ways of solving quadratic equations are good, but many students prefer factoring. It’s simpler, faster, and helps them understand math better.