The easiest way to factor an algebraic expression is to find the greatest common factor, or GCF, and reduce. Factoring is the process of finding what equivalent terms can be multiplied together to find the original expression.
Long, confusing algebraic equations are made more manageable by factoring. Knowing the steps to this method makes the equations easier to work with and understand.
- Find the highest common factor
- Reduce and rewrite
Reduce the original equation by its greatest common factor. This is defined as the largest term that will divide evenly into the problem. For example, the GCF for 10y and 15y is 5y. This is because 5y divides evenly into both: 5y x 2 = 10y and 5y x 3 = 15y. However, the GCF for 12a and 18b would be 6: 6 x 2a = 12a and 6 x 3b = 18b.
Once the GCF for the equation has been determined, reduce the equation by that factor and rewrite. The solution is the product of the GCF and the original expression after factoring. For example, the GCF for 28x4y3 - 42x3y5 is 14x3y3. After factoring, the final answer to this example is 14x3y3(2x - 3y2). To double-check the answer, simply use the multiplication rules for polynomials. The answer should equal the original equation.