The image presents several problems that involve factoring polynomials by finding the Greatest Common Factor (GCF). We are asked to factor the polynomials in the image.

1. Problem Description

The image presents several problems that involve factoring polynomials by finding the Greatest Common Factor (GCF). We are asked to factor the polynomials in the image.

2. Solution Steps

First section:

1. $28c - 12$

The GCF of 28 and 12 is

4. Factoring out 4:

$28c - 12 = 4(7c - 3)$

2. $x^2y + x$

The GCF of $x^2y$ and $x$ is $x$. Factoring out $x$:

$x^2y + x = x(xy + 1)$

3. $10m^2n + 30mn^2 + 5mn$

The GCF of $10m^2n$, $30mn^2$, and $5mn$ is $5mn$. Factoring out $5mn$:

$10m^2n + 30mn^2 + 5mn = 5mn(2m + 6n + 1)$

4. $72a^2b^3c - 32a^3b^2c^2$

The GCF of $72a^2b^3c$ and $32a^3b^2c^2$ is $8a^2b^2c$. Factoring out $8a^2b^2c$:

$72a^2b^3c - 32a^3b^2c^2 = 8a^2b^2c(9b - 4ac)$

Second section:

1. $32m + 20$

The GCF of 32 and 20 is

4. Factoring out 4:

$32m + 20 = 4(8m + 5)$

2. $c^2d - c$

The GCF of $c^2d$ and $c$ is $c$. Factoring out $c$:

$c^2d - c = c(cd - 1)$

3. $12a^2b + 24ab^2 + 6ab$

The GCF of $12a^2b$, $24ab^2$, and $6ab$ is $6ab$. Factoring out $6ab$:

$12a^2b + 24ab^2 + 6ab = 6ab(2a + 4b + 1)$

4. $72m^7n^4p - 32m^3n^3p^3$

The GCF of $72m^7n^4p$ and $32m^3n^3p^3$ is $8m^3n^3p$. Factoring out $8m^3n^3p$:

$72m^7n^4p - 32m^3n^3p^3 = 8m^3n^3p(9m^4n - 4p^2)$

3. Final Answer

First Section:

1. $4(7c - 3)$

2. $x(xy + 1)$

3. $5mn(2m + 6n + 1)$

4. $8a^2b^2c(9b - 4ac)$

Second Section:

1. $4(8m + 5)$

2. $c(cd - 1)$

3. $6ab(2a + 4b + 1)$

4. $8m^3n^3p(9m^4n - 4p^2)$