factor linear expression

1. Identify the greatest common factor (GCF): To factor the expression $6v + 10$, we first look for the greatest common factor of the coefficients $6$ and $10$. The factors of $6$ are $1, 2, 3, 6$. The factors of $10$ are $1, 2, 5, 10$. The largest number that divides both $6$ and $10$ is $2$.

2. Factor out the GCF: We divide each term in the expression by the GCF, which is $2$, and place the GCF outside of a set of parentheses:
$$6v + 10 = 2(3v + 5)$$

1. Verify the result: Distribute the $2$ back into the parentheses to ensure it equals the original expression: $2 \cdot 3v + 2 \cdot 5 = 6v + 10$. The factorization is correct.