Reviewing certain terminology will be vital to factoring, especially at the more basic stages. Some of these terms might include "GCF," "LCM" and "Prime Factor." The GCF is the greatest common factor, or the largest number that multiplies evenly into two numbers. The LCM, or least common multiple, is the smallest number that two numbers share when multiplied by other numbers. Prime factors are a list of the prime numbers (numbers divisible only by themselves and by one) that multiply together to make the original number, without leaving a remainder.
Working through a set of quadratic equations and other algebraic expressions can help students refresh their knowledge of algebra and how it works. Concepts to review include FOIL-ing, in which students working with two sets of numbers in the form (a +/-b) * (a +/-b) multiply the first numbers together, then the outside numbers, then the inside numbers, and finally the last terms together to arrive at an expression in the form of aX^2 + bX + c = 0. Students also should practice reverse FOIL-ing, in which students find the factors of a quadratic equation and put them back into parenthetical form.
Students should work through a series of problems with equations at higher powers than the square. In these cases, they should work on factoring out enough variables to arrive at a quadratic equation. For example, when students see an expression in the form of aX^4 + bX^3 + cX^2 = 0, they can factor out X^2 from each expression and put it outside of a parenthetical to show that it is a factor. In this case, it would be x^2 (aX^2 + bX + c = 0).
To master other aspects of factoring for college algebra, students should become familiar with recognizing perfect squares, sums of two cubes and other such expressions. For example, when factoring a perfect square, the expression a^2 + 2ab+b^2 also can be expressed as the factors (a+b)^2. The sum of two cubes, or x^3 + a^3, can be expressed as (x+a) (x^2 --ax + a^2). Many such expressions exist and can give students time-saving shortcuts on a variety of problems.