Number and Letter Together

The greatest common factor (GCF) is the biggest thing that divides every term. It can have a number and a letter. In $6{x}^{2}+9x$, 3 divides both 6 and 9. Both terms also have an $x$. So the GCF is $3x$.

Divide each term by $3x$: $\frac{6{x}^{2}}{3x} = 2x$ and $\frac{9x}{3x} = 3$. So:

$$6{x}^{2}+9x = 3x\left(2x+3\right)$$