Explain how a four-term polynomial is factored by grouping and when a quadratic trinomial can be factored using this method. include examples in your explanation.

Lets suppose that the 4-term polynomial that is being factored is . 

.  

Factor out common terms in the first two terms, then in the last two terms 

 

Factor out the common term 

 

Now lets factor a quadratic trinomial using this method 

 

Split the second term into two terms 

Multiply the coefficient of the first term by the constant term 

 

Ask yourself: Which two numbers will add up to 10 and multiply to -24? 

 

Split 10x as the sum of 12x and -2x 

 

Factor out common terms in the first two terms, then in the last two terms

 

Factor out the common term x+4

The answer would be a