Skip to content

Factoring Trinomials that have Negatives

November 1, 2018

Algebra tiles are a great help when factoring trinomials.

We looked at a few.  The first question happened to be impossible, but now we know why.  We also were able to modify the question to create other options that are similar that do factor.

We are building rectangles out of these expressions.

Here’s the start of my rectangle.  I look at different ways I can arrange 14 that make rectangles (either 1×14 or 2×7).  I put my units in their rectangular arrangement diagonal to the x squared.


Next I try to fill in the gaps in the rectangle using my x rectangles.


At this point the rectangle is not full, so I’ll add some zero pairs of xs.  I know I need to put the positives so that they will multiply with the negatives to result in negatives in the bottom right corner. 


My rectangle still isn’t full, and if I had arranged my squares 1×14 it would make another rectangle that wouldnt be complete.  We know that this is an impossible question,  but that we could easily make a rectangle out of the following, which simplifies to x^2-2x-8


Or the following, which simplifies to x^2-5x-14.


After a lot of exploring we noticed something that is always true about the numbers in the rectangle and the numbers in the expression.  We are looking for a way to form the constant term into a rectangle with dimensions that will add up to the x coefficient.

No comments yet

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: