Which algebra of the following problems (Polynomials, Factoring, Rational Expressions, Rational Equations, Radical Expressions, Radical Equations, and Quadratic Equations) were the most challenging for you? Why?
What did you learn from the experience, and how did you overcome this challenge? If you could provide some tips or advice to new Algebra students, what would you share with them?
I had trouble learning factoring. When I learned factoring, I was told to simply write two sets of parentheses, put factors of the first term in the first places in each set and factors of the last term in the second places and use the foil method to check until one worked. This was usually easy but I had no sense of what was going on until I had practiced enough. Maybe learning the idea behind factoring before learning the process of factoring would have been more useful to me.
I tutor at a small community college and I've noticed most people have a very hard time factoring. As a consequence, many other types of problems become difficult because of difficulty factoring.
My suggestion would be to master factoring first then completing the square and from that derive the quadratic formula. Those would be most of the tools one would need to solve almost any quadratic equation.