Educational Thoughts, Ideas, and Resources for Teachers

Help Struggling Students Factor Quadratics

It’s the truth! Factoring is a major topic and somehow, we have to make sure students can do it. Factoring is needed for all math classes after Algebra and for all college entrance exams (SAT, PSAT and ACT) and placement exams (ACCUPLACER and TSI). Algebra teachers have enough on their plate without this pressure, but it’s our job to teach it and hopefully it will be reinforced in future math classes.

About ten years ago, one of my coworkers showed me a cool calculator method that I use with struggling students. Some students have a hard time with their multiplication facts which will make factoring a nightmare for them.

I hate most calculator tricks, but this one is actually a great tool. Let’s say a student needs to know all the factors of 135. Have them go to the graph of the calculator and type 135/x (135 divided by x). Next have the student look at the table. In the table, they will look for whole number values. For instance, across from an x of 1, is a y of 135. That of course means that 1 and 135 are factors of 135. The next set of whole number values are x = 3 and y = 45. When the list of numbers starts repeating, all of the factors have been found.

Look at the sample factoring problem below this paragraph. I have my students multiply the 9x^2 and the -15. The answer is -135x^2. To the right of the problem, they draw a large X . On the top, they write the -135x^2 and on the bottom of the X, they write the middle term: 22x. Next, they start making a list of all of the factors of 135. I tell them not to think about the negative at first…just make a list of factors. If they are not able to do that, then use the calculator to make the list. Once the list is made, then the students decide which factors will multiply to get -135 and subtract to get 22. The answer would be 27 and -5. Those two numbers are written on the left and right side of the X. Next, the original trinomial is turned into a polynomial with four terms. The second step below was 9x^2 + 27x – 5x – 15, before I started the grouping process. The problem is grouped and the factors are found. (Yes, I teach grouping. It helps with this type of problem and it helps with factoring out a GCF. Don’t skip grouping. If you’d like to see more about how I teach factoring go to this Factoring Blogpost.)

Here’s a quick video explaining the same problem:

All students can factor! Believe it, teach it and recycle it!