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Question

Factor the polynomial completely.

 

2x²+2ax−x−a=

Answer 1

Hi Seth,

 

The trick to this problem is the use of the distributive property.

 

Let's examine the problem:

 

Factor the polynomial completely  2x²+2ax−x−a=

 

Let's start by gathering all of the terms that contain a, which are 2ax and −a.

 

They factor into a*(2x-1)

 

Now let's look at the remaining terms of 2x² and -x and combine them into x(2x-1)

 

Note that both terms inside the parentheses are equal and the equation can be rewritten as

 

 2x²+2ax−x−a= a*(2x-1) + x(2x-1) or

 

2x²+2ax−x−a= (2x-1)*(a+x) which is the form of the final factor