Checking your work after factoring a quadratic equation is really important. It helps to make sure you didn’t make any mistakes. Here’s how I usually do it:

1. Write Down the Factors: After you’ve factored the quadratic (like changing $ax^2 + bx + c$ into something like $(x + p)(x + q)$), be sure to write it down clearly.

2. Expand It Back: Here is where the fun starts! Take your factors and multiply them back out. This helps you see if you get the original quadratic. For example, if you factored it to $(x + 2)(x + 3)$, multiply it out to get $x^2 + 5x + 6$.

3. Compare the Results: Check to see if your expanded version matches the original quadratic. Look closely at the numbers in front of $x$ and the constant term. If everything matches, you did it right!

4. Use the Quadratic Formula (optional): You can also solve the original equation using the quadratic formula, which is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Then, check if the answers you found in your factors match up.

By following these steps, I always feel much more sure that I’ve got the right answer!