If you have 2 terms and no GCF, what is a potential option for quick factoring?

Question

I'm sorry this was a question on a review sheet

Answer 1

Examples of factoring when there are only 2 terms:   difference of two squares and sum of 2 cubes.

 

a² - b² = (a-b)(a+b)   So, x² - 81 = x² - 9²

 

                                               = (x-9)(x+9)

 

a³ + b³ = (a+b)(a²-ab+b²)

 

   So, x³ + 125 = x³ + 5³ = (x+5)(x²-5x+25)

 

 

 

Answer 2

I would use factoring by grouping.  If you have an expression in which the only common factor among the terms is 1, then group each term according to a common factor.  Then you will factor each group using the common factor.  Once you do that, you will see a binomial factor in which the terms have in common.  The binomial term is the common factor.

 

Here is an example of what I mean.

 

x² + 5x - 3x - 15        ---->  the common factor of each term is 1.

 

x(x + 5) - 3(x + 5)   ----> grouping terms by common factor.

 

(x - 3)(x + 5)         ---->  the binomial (x + 5) is the common factor binomial.