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.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.  