Factor.

To factor the quadratic expression , we are looking for two numbers that multiply to 20 (the constant term) and add to 12 (the coefficient of the linear term). Those two numbers are 10 and 2 because and . Therefore, we can factor the expression as:

Now you have it in a neat and factored form!

For an added touch of fun, did you know that the quadratic formula, which is a lifesaver for factoring when you can’t see the factors quickly, is derived from completing the square? It’s a great tool to use when factors are sneaky! If your quadratic doesn’t factor nicely, just plug the numbers into this formula: .

And if you’re looking to flex your math muscles a bit more, consider exploring the world of polynomial factorization! There are some fascinating methods like synthetic division or the Rational Root Theorem that can come in handy. Books on algebra are a treasure chest of these techniques!