Chapter 7: Factoring
7.2 Factoring by Grouping
First thing to do when factoring is to factor out the GCF. This GCF is often a monomial, like in the problem where the GCF is the monomial , so you would have . However, a GCF does not have to be a monomial; it could be a binomial. Consider the following two examples.
Example 7.2.1
Find and factor out the GCF for .
By observation, one can see that both have in common.
This means that .
Example 7.2.2
Find and factor out the GCF for .
Both have as a common factor.
This means that if you factor out , you are left with .
The factored polynomial is written as .
In the same way as factoring out a GCF from a binomial, there is a process known as grouping to factor out common binomials from a polynomial containing four terms.
Find and factor out the GCF for .
To do this, first split the polynomial into two binomials.
becomes and .
Now find the common factor from each binomial.
has a common factor of and becomes .
has a common factor of 2 and becomes .
This means that .
can be factored as .
Questions
Factor the following polynomials.