D. Factoring More Complicated Trinomials

The strategies shown throughout this Lesson can be combined to factor more complex trinomials of the form ax2+bx+c.

Trinomials with a GCF

If the GCF of a trinomial is something other than 1, the GCF can be factored out first and the resulting trinomial can be expressed as a product of two binomial factors. Removing the GCF first will make the resulting trinomial easier to factor.

Example 1

Factor .

The terms of this trinomial have a GCF of 3. However, since all three terms of the trinomial are negative, remove –3 as a common factor.

Now, factor the resulting trinomial. The integers 5 and 6 add to 11 and have a product of 30.

Notice that determining two integers that add to 11 and have a product of 30 is much easier than determining two integers that add to -33 and have a product of 270. By factoring out the -3 first, the numbers are easier to work with.

 

Remember to always carry the GCF through all the steps of your work. It is very easy to forget and leave it behind.

 

Trinomials with Multiple Variables

Some trinomials that contain multiple variables can also be factored using the strategies outlined earlier in this lesson.

Example 2

Factor .

ac = −6 and b = 5

The integers 6 and −1 have a product of −6 and a sum of 5. Decompose the term 5xy using these values.