Most students find factoring fairly straight forward when first introduced. An equation might look like **x ^{2}+6x+9 **and be factored to (x+3)(x+3). But what happens when we see a coefficient to

**x**that is not 1? This is where factoring by grouping comes into play.

^{2}Here’s an example: **4x ^{2}+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:

**4x ^{2}+-2x+18x-9**

Then we’ll group them to: (**4x ^{2}+-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.