Factor out the Greatest Common Factor (GCF) from each expression. If the expression is prime, write "prime."

1) [tex]\( 16p^3 + 4p^5 \)[/tex]
GCF: [tex]\( 4p^3 \)[/tex]
Factored: [tex]\( 4p^3(4p + 1) \)[/tex]

2) [tex]\( 9x + 36 \)[/tex]
GCF: [tex]\( 9 \)[/tex]
Factored: [tex]\( 9(x + 4) \)[/tex]

3) [tex]\( 63 + 45b \)[/tex]
GCF: [tex]\( 9 \)[/tex]
Factored: [tex]\( 9(7 + 5b) \)[/tex]

4) [tex]\( 6n^3 - 3n^5 \)[/tex]
GCF: [tex]\( 3n^3 \)[/tex]
Factored: [tex]\( 3n^3(2 - n^2) \)[/tex]

5) [tex]\( -6r^5 - 6r^4 \)[/tex]
GCF: [tex]\( -6r^4 \)[/tex]
Factored: [tex]\( -6r^4(r + 1) \)[/tex]

6) [tex]\( 63x^{12} - 35x^6 \)[/tex]
GCF: [tex]\( 7x^6 \)[/tex]
Factored: [tex]\( 7x^6(9x^6 - 5) \)[/tex]

7) [tex]\( 14a + 21a^2 + 21a^3 \)[/tex]
GCF: [tex]\( 7a \)[/tex]
Factored: [tex]\( 7a(2 + 3a + 3a^2) \)[/tex]

8) [tex]\( 10n^3 - 9n^2 + n \)[/tex]
GCF: [tex]\( n \)[/tex]
Factored: [tex]\( n(10n^2 - 9n + 1) \)[/tex]

9) [tex]\( -8x^7 + 24x^6 + 12x^5 \)[/tex]
GCF: [tex]\( 4x^5 \)[/tex]
Factored: [tex]\( 4x^5(-2x^2 + 6x + 3) \)[/tex]

10) [tex]\( 9x^6 - 63x^3 - 90x^2 \)[/tex]
GCF: [tex]\( 9x^2 \)[/tex]
Factored: [tex]\( 9x^2(x^4 - 7x - 10) \)[/tex]

11) [tex]\( 50p^3 + 50p^2 - 20 \)[/tex]
GCF: [tex]\( 10 \)[/tex]
Factored: [tex]\( 10(5p^3 + 5p^2 - 2) \)[/tex]

12) [tex]\( -90x^5 + 100x + 60 \)[/tex]
GCF: [tex]\( 10 \)[/tex]
Factored: [tex]\( 10(-9x^5 + 10x + 6) \)[/tex]

13) [tex]\( 12r^2 + 4r - 12 \)[/tex]
GCF: [tex]\( 4 \)[/tex]
Factored: [tex]\( 4(3r^2 + r - 3) \)[/tex]

14) [tex]\( -18n^2 + 15n - 15 \)[/tex]
GCF: [tex]\( 3 \)[/tex]
Factored: [tex]\( 3(-6n^2 + 5n - 5) \)[/tex]

15) [tex]\( 0x^2 + 72x \)[/tex]
GCF: [tex]\( 72x \)[/tex]
Factored: [tex]\( 72x(1) \)[/tex]

16) [tex]\( 3k^3 + 15k^2 - 6k \)[/tex]
GCF: [tex]\( 3k \)[/tex]
Factored: [tex]\( 3k(k^2 + 5k - 2) \)[/tex]

17) [tex]\( 28n - 20 \)[/tex]
GCF: [tex]\( 4 \)[/tex]
Factored: [tex]\( 4(7n - 5) \)[/tex]

18) [tex]\( 9m + 27 \)[/tex]
GCF: [tex]\( 9 \)[/tex]
Factored: [tex]\( 9(m + 3) \)[/tex]

Let's go through the process of factoring out the Greatest Common Factor (GCF) for some of these expressions step by step.

### Expression 1: [tex]\( 16p \cdot p \cdot P + 4p^2P \cdot P \cdot P \)[/tex]

#### Steps:
1. Identify Common Terms: Both terms contain factors of [tex]\( p \)[/tex] and [tex]\( P \)[/tex].
2. Calculate GCF for Coefficients: GCF of 16 and 4 is 4.
3. Determine the Smallest Power for Each Variable:
- For [tex]\( p \)[/tex], both terms have at least [tex]\( p^2 \)[/tex].
- For [tex]\( P \)[/tex], both terms have [tex]\( P \)[/tex].

4. Combine the GCF:
[tex]\[
\text{GCF} = 4p^2P
\][/tex]

5. Factor Out the GCF:
[tex]\[
4p^2P (4pP + P^2)
\][/tex]

Simplified:
[tex]\[
4p^2P (4P + P)
\][/tex]

### Expression 3: [tex]\( 63 + 45b \)[/tex]

#### Steps:
1. Calculate GCF for Coefficients:
- GCF of 63 and 45 is 9.

2. Factor Out the GCF:
[tex]\[
9(7 + 5b)
\][/tex]

### Expression 5: [tex]\( -6r^5 - 6r^4 \)[/tex]

#### Steps:
1. Identify Common Factor:
- Both terms share [tex]\( -6r^4 \)[/tex].

2. Factor Out the GCF:
[tex]\[
-6r^4(r + 1)
\][/tex]

### Additional Guidance

- When factoring expressions, always look for the largest factor shared by all terms.
- Write down the smallest exponent for variables that appear in each term.
- Simplify what's inside the parentheses after factoring out the GCF.

Let me know if you have any questions or need assistance with any other part of the work!