Just like it says, factoring by grouping means that you will group terms with common factors before factoring.

This is done by grouping a pair of terms. Then, factor each pair of two terms.

I will illustrate this with a simple example

Factor x

The expression x

has three terms right now, so we need to write it with 4 terms before we can group terms.

Notice that 5x = 3x + 2x, so x

Group x

(x

In this example, if you group x

Notice that there is more than one way we can expand 5x, so different groupings are possible.

5x is also equal to 4x + x, 6x -x, 7x-2x, 8x-3x, and so forth...

However, only one grouping will work

This brings light to the fact that this way of factoring by grouping can be very tedious sometimes.

Although it is always good to know, it is not always a straightforward method to factor trinomials

x

At first, you may be tempted to say that -4x can be equal to: -2x + -2x, or -3x + -x, so one of them will work

Wrong! The right combination is -6x + 2x

So, x

Group x

(x

3y

3y

So, 3y

11x

This problem is very complicated because you have too many choices for things you can add to get -41x

Some possibilities are:

.....

.....

-46x + 5x

-45x + 4x

-44x + 3x

-40x + -1x

-39x + -2x

-38x + -3x

-36x + -4x

.....

.....

It turns out that the right combination is - 44x + 3x

There is good news though since there is a technique to use to find the right combination a little bit faster when factoring by grouping.

Do 11 * -12 = -132

Then, find factors of -132 that will add up to -41

The factors are -44 and 3

11x

11x

6x

6 * 28 = 168

-14 + -12 = -26 and -14 * -12 = 168, so the right combnation is

6x

6x

6x

Use factoring by grouping only if you have no other choices!