Factoring by Grouping

Factoring by grouping is often used when given a polynomial with more than 3 values. With this method, you will split the polynomial into separate parts and factor them individually, then simplifying in the end.

Example:

x^3 + 2x^2 + 4x + 8

First splitting the expression into two parts, x^3 + 2x^2 and 4x + 8 and factoring separately:

= x^2(x + 2) + 4(x + 2)

You will then factor out the common factor of the two terms, in this case being x + 2. It may look confusing with the x + 2, but in reality it is not that hard. Another way you could write this expression to make it seem less confusing is by letting x + 2 equal a variable:

Let (x + 2) = A

x^2A + 4A

Now, it may be easier to see the common factor, and you would proceed as you do with any normal factoring question of this kind, factoring out A.

= A(x^2 + 4)

What was in the brackets is simply another factor to the overall terms and should be treated as such. Keep in mind that if you do use the strategy of replacing it with a variable, you must always revert it back to its original form when writing your final answer.

= (x + 2)(x^2 + 4)