With this equation,
, we will do our first example of factoring by grouping.
First we will notice that there isn’t an opportunity to factor anything out of all the
terms because there isn’t enough in common in this equation. So the systematic next step
we will take is grouping our equation into things with like terms. The first two terms
group nicely, and the third and fourth term go together the best because 2x can be taken
out of the first two terms, and in the second grouping 3 can be taken out. This would be shown
like this:
. Then as we factor out the 2x and 3 the equation would look like this:
2x(x+4)+3(x+4). In doing this step we can find another common factor between the terms; They both have x+4 in parenthesis.
This can be simplified with distributive properties. So the end result will look like this instead:
(x+4)(2x+3). When we did this step we combined the x+4 into one set of parenthesis, and took the numbers
before the parenthesis and combined them into a new set of parenthesis that can then multiply to make the original equation.
Example 2:
This example will be given with this equation:
First we group like we did last time into two parenthesis.
Then we take out the greatest common factors: 3x(x+2)+4(x+2)
With this we again realize that there is
another set of common factors within this equation. We distribute the x+2 into the following section and combine the
outside numbers to create the ending equation of (x+2)(3x+4)
There are many different strategies for figuring out grouping of your polynomials.
Below is a video of the x method. This is another method of grouping, but it is done in a more understandable way.