Factoring is considered to be one of the essential processes to simplify many algebraic expressions, and it is a handy tool for solving any higher degree equations. In fact, factoring process is so important that little of algebra beyond this point get accomplished without understanding this phenomenon. In earlier chapters, you might have discovered the distinctions between the terms and factors which have been very much stressed. Factor polynomials are necessary and you might have wondered that terms refer to addition or subtraction and factors are multiplied or divided. Three of the most important form is as follows:
• Terms that occur in indicated sum or differences
• Factors that occur at an indicated product
• An expression that is in factored form when an entire expression is in indicated product
Sometimes you don’t get to know if the form is factored or not in factored form, in such troubles, recall these examples: 6x(x + 3y), (2x + 3y)(4x – 2y), and (4x + 1)(x2 + 6x – 8) are some examples of factored form while 2x + 3y + z, 2(x + y) +z, and (x + y)(2x – y) + 5 are some example of non factored form. Note through these examples that you must always regard the entire expression. Some factors made up of terms that can contain factors but factored forms are mainly those that must confront with the above examples. Factoring is a process that helps in changing expression from terms like sum or differences to a product of factors.
Remove common factors:
Objectives are to determine the factors that are common to all terms of expression and factor common factors. To learn about this method, go through this example-
Example: factor 2x^2 + 6xy + 8xy^2
Solution: first, look for the factors of each term: 2x^2 comprises with the factors 1, 2, x, x^2, 2x, and 2x^2, 6xy with 1, 2, 3, 6, x, 2x, 3x, 6x, y, 6xy, 6y, and 8xy^2 with factors 1, 2, 4, 8, x, 2x, 4x, and so on. Here, you can see that 2x is common in all the factors. Now, take out this common from the expression and proceed by placing 2x to the set of parentheses.
2x ( )
Within the term, place the parentheses by dividing the whole expression by the 2x, then it will give expression to be: 2x (x + 3y + 4y^2)
Note: this is based on a distributive property. So it is the reverse of the processes you have learned until now. You may think factored form to be 2(x^2 + 3xy + 4xy^2) which is wrong as it is not fully factored. You should be sure to factor expressions completely which is why it is best to choose the largest common factor. Many students don’t get greatest common factor because they are not careful. A factor is that part where you need to practice a lot. Find out examples and questions from exercise to be perfect in this region. Factor polynomials are considered to be one of the best ways to get perfect in solving any equation based expressions.