Factoring by grouping

Most students find factoring fairly straight forward when first introduced. An equation might look like x2+6x+9 and be factored to (x+3)(x+3). But what happens when we see a coefficient to x2 that is not 1? This is where factoring by grouping comes into play.

Here’s an example: 4x2+16x-9

First, we need to find factors of the product of the a term (4) and the c term (-9) that add up to the b term (16). So first multiply 4*-9. We get -36. Now, let’s look at all factors of -36 and find two that add up to 16. 1 and -36? No, that equals -35. How about 18 and -2? Yes, they add up to 16.

So, now let’s split up the middle term, 16x, into those two terms and “group” them:

4x2+-2x+18x-9

Then we’ll group them to: (4x2+-2x)+(18x-9)

Now factor the groups:

2x(2x-1)+9(2x-1)

Now, using the distributive rule we can simplify it to:

(2x+9)(2x-1)

If the last step was confusing, try foiling (2x+9)(2x-1) and see that it gets you the original equation.

Factoring by grouping

By Silver Spoon (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons