On a separate sheet of paper, complete the questions below pertaining to GCF and factoring trinomials when [tex]a=1[/tex]. You must show your work.

Factor using GCF

11) [tex]20 - 35n^2 - 20n^3[/tex]

12) [tex]9x^6 - 63x^3 - 90x^2[/tex]

13) [tex]-3k^3 + 15k^2 - 6k[/tex]

14) [tex]50p^3 + 50p^2 - 20[/tex]

15) [tex]32n^3 + 28n - 20[/tex]

16) [tex]-90x^5 + 100x + 60[/tex]

Sure! Let's go through the process of factoring each expression to find the Greatest Common Factor (GCF) and simplify.

### 11) [tex]\( 20 - 35n^2 - 20n^3 \)[/tex]

1. Identify the GCF: The GCF of the coefficients 20, 35, and 20 is 5.
2. Factor out the GCF:
[tex]\[
20 - 35n^2 - 20n^3 = 5(4 - 7n^2 - 4n^3)
\][/tex]

### 12) [tex]\( 9x^6 - 63x^3 - 90x^2 \)[/tex]

1. Identify the GCF: The GCF of the coefficients 9, 63, and 90 is 9. The lowest power of [tex]\( x \)[/tex] is [tex]\( x^2 \)[/tex].
2. Factor out the GCF:
[tex]\[
9x^6 - 63x^3 - 90x^2 = 9x^2(x^4 - 7x - 10)
\][/tex]

### 13) [tex]\( -3k^3 + 15k^2 - 6k \)[/tex]

1. Identify the GCF: The GCF of the coefficients -3, 15, and -6 is 3. The lowest power of [tex]\( k \)[/tex] is [tex]\( k \)[/tex].
2. Factor out the GCF:
[tex]\[
-3k^3 + 15k^2 - 6k = -3k(k^2 - 5k + 2)
\][/tex]

### 14) [tex]\( 50p^3 + 50p^2 - 20 \)[/tex]

1. Identify the GCF: The GCF of the coefficients 50, 50, and 20 is 10.
2. Factor out the GCF:
[tex]\[
50p^3 + 50p^2 - 20 = 10(5p^3 + 5p^2 - 2)
\][/tex]

### 15) [tex]\( 32n^3 + 28n - 20 \)[/tex]

1. Identify the GCF: The GCF of the coefficients 32, 28, and 20 is 4.
2. Factor out the GCF:
[tex]\[
32n^3 + 28n - 20 = 4(8n^3 + 7n - 5)
\][/tex]

### 16) [tex]\( -90x^5 + 100x + 60 \)[/tex]

1. Identify the GCF: The GCF of the coefficients -90, 100, and 60 is 10.
2. Factor out the GCF:
[tex]\[
-90x^5 + 100x + 60 = -10(9x^5 - 10x - 6)
\][/tex]

These are the factored forms of the given expressions using their Greatest Common Factors.