COMMON FACTORS

Common factoring is the opposite of "expanding and simplifying" as you are only "simplifying" the expression and not "expanding" it, (you are finding the expresion to multiply instead of multiplying the expressions). Here are three types of factoring...

Greatest Common Factoring

One easy method for solving any polynomials is to first find the "Greatest Common Factor" (GCF). One example for finding this is here, You will recieve two terms (-12xy) and (-6x). As we talked about before (GCF), the greatest common factor from the two numbers is "6" as this number is the highest number that can fit through these two expressions. (If a negative is included in these two numbers then you would add a negative beside your answer, (vice versa if your numbers were positive). finally for varaibles, you find the smallest exponent of the variable that matches between two expressions. There is only one variable that is different from the "x's" which is "y". therefore the final factored form will be (-6x).

Monomial Factoring

Simple

Here in monomial factoring is usually a three step process. First, you would find the greatest common factor which is "x" as "8" and "7" don't have a (GCF). your final answer woud have been "x(8x-7).

Complex

When factoring with three or more terms, you would do the same thing as you did above, find the (GCF) for all three terms in this expression which is "2" and find the same variable that are from the three expressions which is x^2. Your final factored form is if you cannot factor the expression anymore which is "2x^2(4-3y^2+2y)". If by any chance you recieve a variables with different square numbers, you would find the lowest square number and subtract the squared number with the other squares (only for the common variable in all three or more expressions.

Binomial Factoring

In binomial factoring you would take anything inside the brackets of expressions and group them in one place and the rest outside which are "5x" and "4" you would pit them on another side giving you "(3x+2)(5x+4).

Factor By Grouping

Finally, "(ax+ay) and (2x+2y)" you would find the common factor from each of those two expressions and leave them outside the bracket which are "a" and "2". after you will recieve two identical expressions inside the brackets and group them making (x+y). on to other side group your uncommon terms together making you final factored form "(x+y)(a+2)". The plus sign that intersects the two bracket expressions determines if the first number inside the second bracket is positive which it is (vice versa if the positive were to be a negative).