The problem requires matching linear expressions with their greatest common factor (GCF). The expressions are $8x + 6$, $25 + 5b$, $12xy + 8x$, and $6a + 12$. The possible GCFs are $4x$, $2$, $5$, and $6$.

1. Problem Description

The problem requires matching linear expressions with their greatest common factor (GCF). The expressions are $8x + 6$, $25 + 5b$, $12xy + 8x$, and $6a + 12$. The possible GCFs are $4x$, $2$, $5$, and $6$.

2. Solution Steps

We will find the GCF for each expression.

* $8x + 6$: The factors of 8 are 1, 2, 4, and

8. The factors of 6 are 1, 2, 3, and

6. The GCF of 8 and 6 is

2. Therefore, $8x + 6 = 2(4x + 3)$. The GCF is

2.

* $25 + 5b$: The factors of 25 are 1, 5, and

2

5. The factors of 5 are 1 and

5. The GCF of 25 and 5 is

5. Therefore, $25 + 5b = 5(5 + b)$. The GCF is

5.

* $12xy + 8x$: The factors of 12 are 1, 2, 3, 4, 6, and

1

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

8. The GCF of 12 and 8 is

4. Both terms have $x$ as a factor. Thus, the GCF is $4x$. Therefore, $12xy + 8x = 4x(3y + 2)$. The GCF is $4x$.

* $6a + 12$: The factors of 6 are 1, 2, 3, and

6. The factors of 12 are 1, 2, 3, 4, 6, and

1

2. The GCF of 6 and 12 is

6. Therefore, $6a + 12 = 6(a + 2)$. The GCF is

6.

3. Final Answer

The matches are:

* $8x + 6$ matches with GCF = 2

* $25 + 5b$ matches with GCF = 5

* $12xy + 8x$ matches with GCF = $4x$

* $6a + 12$ matches with GCF = 6