Factoring Polynomials Part 2:

There are 6 methods that can be used when factoring polynomials. The next 3 methods are AC, Grouping and SOAP. 

AC

When using AC for factoring polynomials, the requirement for using AC is that there have to be 3 terms, the first does not have to equal to 1 and can be greater than 1. Also, when you multiply the first and last term and use the AM method. You would then divide the end by the first term that went away. For example, the polynomial 6x^2 + x - 15. First, you would multiply the a and c terms. The a term is 6 and the c is -15. It would equal to -90. Then you would use the AM method meaning that you would need to find two terms that multiply to -90 but add to make the b term and the b term is 1 because there it’s the coefficient of the middle term. The two numbers that multiply to -90 and add to 1 would be 10 and -9 because 10 times -9 equals -90 and 10 + -9 equals 1 which means that it fits perfectly and those are the correct numbers. Once you find the two numbers you would need to take them and split up the middle term using the new two terms so it would be 6x^2 + 10x - 9x - 15. Now you can factor by group which is another method that is used when factoring. You would need to group the first two terms and the second last two terms together. Look at the 1 group of two terms and use GCF and find something in common and in this case 6x^2 + 10x have 2x in common which means that 2x is the GCF. So, it would be 2x(3x+5). For the next two terms do the same thing and continue using GCF and what -9x -15 have in common is -3. So, it would be -3(3x+5). Together it would be 2x(3x+5)-3(3x+5). You can see that there is something in common and that is the 3x+5 which means that you would need to factor out 3x+5. Then, you would have (3x+5)(2x-3). To get (2x-3) you would be taking the 2x and -3 in front of the (3x+5). To check your work you can just multiply (3x+5) and (2x-3) and you would get 6x^2 + x - 15. 

Grouping:

Grouping is a method used to factor and was used when using the method AC. The requirement for using grouping when factoring is that there have to be 4 terms. When grouping you would need to group the 1 and 2nd term in order to find the GCF and you would have to group the 3rd and 4th term and also find the GCF. An example would be 3x^2 + 6x + 4x + 8. You would group (3x^2 + 6x) and (4x + 8) and find the GCF. For (3x^2 + 6x) the GCF is 3x, so it would be 3x(x+2). For (4x + 8) the GCF is 4, so it would be 4(x+2). Then you can see that what they have in common is (x+2) so you would factor (x+2). In the end, your answer will be (x+2) (3x+4) because you would take the terms in front of (x+2) and put them together.