Factoring trinomials in this form : 

To do this by inspection you need to find two integers which have a product of c and a sum equal to b.

Example: 

You need to identify what two numbers have a product of 20 and has a sum of 21. In many this case 20 has many possibilities for the sum and a product,, this can be a challenge. For example 4 & 5 equals to 20 as a product, however their sum is only 9 so that wouldn’t work. What would work though would be 1,20, because they make a product of 20 and have a sum of 21. Then what you need to do is factor and write out the equation

 = 

You know that this is correct when you foil the term and get the same equation.

I earned to factor a polynomial by removing the greatest common factor.

In this equation the common factor is .
  Since  is a factor of both the terms you divide it to get it’s simplest form.

You know you have done it correctly if you can go the other way around and get the same equation.