The problem asks to factor the linear expression $14m + 35mn$. We are given four options: $7m(2+5n)$, $7m(5+2n)$, $m(14+35n)$, and $7(2m + 5mn)$.

1. Problem Description

The problem asks to factor the linear expression $14m + 35mn$. We are given four options: $7m(2+5n)$, $7m(5+2n)$, $m(14+35n)$, and $7(2m + 5mn)$.

2. Solution Steps

We need to find the greatest common factor (GCF) of the terms $14m$ and $35mn$.

The factors of 14 are 1, 2, 7, and

1

4. The factors of 35 are 1, 5, 7, and

3

5. The GCF of 14 and 35 is

7. Both terms have the variable $m$. Therefore, the GCF of $14m$ and $35mn$ is $7m$.

Now, we can factor out $7m$ from the expression:

$14m + 35mn = 7m(2) + 7m(5n) = 7m(2 + 5n)$

3. Final Answer

The factored expression is $7m(2+5n)$.