The problem asks to factor the linear expression $30 - 8d$. We need to identify an equivalent expression from the given options.

1. Problem Description

The problem asks to factor the linear expression $30 - 8d$. We need to identify an equivalent expression from the given options.

2. Solution Steps

We are given the expression $30 - 8d$. We need to find a common factor between 30 and

8. The factors of 30 are 1, 2, 3, 5, 6, 10, 15,

3

0. The factors of 8 are 1, 2, 4,

8. The greatest common factor (GCF) of 30 and 8 is

2. We can factor out 2 from the expression:

$30 - 8d = 2(15 - 4d)$

Now let's check the given options:

1) $4(6 - 2d) = 24 - 8d$. This is not equal to $30 - 8d$.

2) $2(15 - 4d) = 30 - 8d$. This is equal to the original expression.

3) $2(15d - 4) = 30d - 8$. This is not equal to $30 - 8d$.

4) $8(4 - d) = 32 - 8d$. This is not equal to $30 - 8d$.

3. Final Answer

The factored expression is $2(15 - 4d)$.