Greatest Common Factor (GCF) is the largest number that each term has in common.

Question

You can also think of it as the LARGEST number that you can divide each term by.

What is the GCF of
9x2+15x?

Answer 1

To find the Greatest Common Factor (GCF) of the expression \(9x^2 + 15x\), we can follow these steps:

1. Factor out the coefficients:

   • The coefficients are 9 and 15.
   • The GCF of 9 and 15 can be found by listing their factors:
     • Factors of 9: 1, 3, 9
     • Factors of 15: 1, 3, 5, 15
   • The largest common factor is 3.

2. Factor out the variable:

   • The terms \(x^2\) and \(x\) have a common variable factor of \(x\).
   • The lowest power of \(x\) that appears in both terms is \(x\) (since \(x^2\) has \(x\) and \(x\) has \(x^1\)).

3. Combine the GCF of the coefficients and the variable:

   • The GCF of the whole expression is \(3x\).

4. Final Expression: Now we can express \(9x^2 + 15x\) as: \[ 9x^2 + 15x = 3x(3x + 5) \]

Thus, the GCF of \(9x^2 + 15x\) is \(3x\).