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!