how to factor variables?

Question

Factor the polynomial completely.

x²+3x+ax+3a

Answer 1

We can factor this expression by grouping:

 

x² + 3x + ax + 3a

(x² + 3x) + (ax + 3a)

x(x + 3) + a(x + 3)

 

So, our factors are:

 

(x + a)(x + 3)

 

We can check our answer by multiplying the two factor together (i.e., FOIL):

 

x² + 3x + ax + 3a