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I'm going to assume that you know how to factor the basic stuff like trinomials and the difference of two squares...

What you really need for Calculus 1 is what I'm going to show you here.  This is a very specific type of factoring that will pop up when you have to clean up your answers on a certain Calculus technique.  With that in mind, the following examples are designed with some unique patterns.

Let's start with some really easy stuff to get you into the pattern of what's going on.

Factor5k + 6k^2  =  k( 5 + 6k )

This one has the same pattern:

 
Factor
5( x - 2 ) + 6( x - 2 )^2  =  ( x - 2 )[ 5 + 6( x - 2 )]  =  ( x - 2 )( 6x - 7 )

 


TRY IT:

Factor5( x + 3 ) + 6( x + 3 )^2