Find the greatest common factor of the terms of the polynomial. $$ 8 v^{4}+18 v^{3} $$

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To find the greatest common factor (GCF) of the terms of the polynomial $$ 8 v^{4} + 18 v^{3} $$, we will follow these steps:

1. **Identify the coefficients and variables of each term**:
   - The first term is $$ 8 v^{4} $$ with a coefficient of $$ 8 $$ and a variable part of $$ v^{4} $$.
   - The second term is $$ 18 v^{3} $$ with a coefficient of $$ 18 $$ and a variable part of $$ v^{3} $$.

2. **Find the GCF of the coefficients**:
   - The coefficients are $$ 8 $$ and $$ 18 $$.
   - The factors of $$ 8 $$ are $$ 1, 2, 4, 8 $$.
   - The factors of $$ 18 $$ are $$ 1, 2, 3, 6, 9, 18 $$.
   - The common factors are $$ 1 $$ and $$ 2 $$.
   - Therefore, the GCF of the coefficients is $$ 2 $$.

3. **Find the GCF of the variable parts**:
   - The variable parts are $$ v^{4} $$ and $$ v^{3} $$.
   - The GCF of $$ v^{4} $$ and $$ v^{3} $$ is $$ v^{3} $$ (the lowest power of $$ v $$).

4. **Combine the GCF of the coefficients and the variable parts**:
   - The overall GCF is $$ 2v^{3} $$.

Thus, the greatest common factor of the terms of the polynomial $$ 8 v^{4} + 18 v^{3} $$ is $$ \boxed{2v^{3}} $$.
The greatest common factor is $$ 2v^{3} $$.

Find the greatest common factor of the terms of the polynomial. \[ 8 v^{4}+18 v^{3} \]

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