Factor out the greatest common factor.

Question

20x^{2 +} 15x

Answer 1

The factors of 20x² (all the values that will divide into 20x²:  

  1, 2, 4, 5, 10, 20, x, 2x, 4x, 5x, 10x, 20x, x², 2x², 4x², 10x², 20x²

 

The factors of 15x:

  1, 3, 5, 15, x, 3x, 5x, 15x

 

The greatest ("largest") one that is common ("in both lists"):

   5x

 

So, with the 5x factored out:    5x(4x+3)

Answer 2

To handle this problem look at the numbers and the variables separately.

 

First, find the greatest common factor(GCF) of 20 and 15.  20 and 15 are both multiples of 5 and that is the largest number that goes into both, so the GCF is 5.

 

Second, find the greatest common factor of the x variables, x² and x.  Remember, x² is x·x, so x is a factor of both.  Therefore the GCF is x

 

Multiplying the GCFs gives the GCF of the whole expression, 5x.

 

Factoring the GCF means dividing out the GCF from each term, so 20x²÷5x is 4x and 15x÷5x is 3. 

 

Finally, you write the GCF in from of the "divided" binomial:

 

5x(4x+3)