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Answer :
To find the greatest common factor (GCF) of the given polynomials, let's break down each expression and identify the GCF.
### 11) [tex]\(21 - 49x + 49x^3\)[/tex]
The coefficients are: 21, -49, and 49.
- List the factors: 21 (1, 3, 7, 21), -49 (1, 7, 49), 49 (1, 7, 49).
- The greatest common factor for these coefficients is 7.
### 12) [tex]\(60n^4 - 80n^3 + 90n^2\)[/tex]
The coefficients are: 60, -80, and 90.
- List the factors: 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), -80 (1, 2, 4, 5, 8, 10, 20, 40, 80), 90 (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).
- The greatest common factor for these coefficients is 10.
### 13) [tex]\(36v^8 + 60v^4 - 18v\)[/tex]
The coefficients are: 36, 60, and -18.
- List the factors: 36 (1, 2, 3, 4, 6, 9, 12, 18, 36), 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), -18 (1, 2, 3, 6, 9, 18).
- The greatest common factor for these coefficients is 6.
### 14) [tex]\(-28b^4 + 49b^3 + 63b\)[/tex]
The coefficients are: -28, 49, and 63.
- List the factors: -28 (1, 2, 4, 7, 14, 28), 49 (1, 7, 49), 63 (1, 3, 7, 9, 21, 63).
- The greatest common factor for these coefficients is 7.
### 15) [tex]\(21a^2 - 7a - 21\)[/tex]
The coefficients are: 21, -7, and -21.
- List the factors: 21 (1, 3, 7, 21), -7 (1, 7), -21 (1, 3, 7, 21).
- The greatest common factor for these coefficients is 7.
### 16) [tex]\(-12x^3 - 2x + 20\)[/tex]
The coefficients are: -12, -2, and 20.
- List the factors: -12 (1, 2, 3, 4, 6, 12), -2 (1, 2), 20 (1, 2, 4, 5, 10, 20).
- The greatest common factor for these coefficients is 2.
### 17) [tex]\(-7n^2 + 56n + 42\)[/tex]
The coefficients are: -7, 56, and 42.
- List the factors: -7 (1, 7), 56 (1, 2, 4, 7, 8, 14, 28, 56), 42 (1, 2, 3, 6, 7, 14, 21, 42).
- The greatest common factor for these coefficients is 7.
### 18) [tex]\(9 - 9p^2 - 3p^5\)[/tex]
The coefficients are: 9, -9, and -3.
- List the factors: 9 (1, 3, 9), -9 (1, 3, 9), -3 (1, 3).
- The greatest common factor for these coefficients is 3.
### 19) [tex]\(30x^4 - 60x^3 - 48x^2 + 48x\)[/tex]
The coefficients are: 30, -60, -48, and 48.
- List the factors: 30 (1, 2, 3, 5, 6, 10, 15, 30), -60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), -48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48), 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48).
- The greatest common factor for these coefficients is 6.
### 20) [tex]\(6x^2 + 21x^4 + 6x^5 - 12x^4\)[/tex]
The coefficients are: 6, 21, and -12.
- List the factors: 6 (1, 2, 3, 6), 21 (1, 3, 7, 21), -12 (1, 2, 3, 4, 6, 12).
- The greatest common factor for these coefficients is 3.
These GCF values correspond to the polynomials provided.
### 11) [tex]\(21 - 49x + 49x^3\)[/tex]
The coefficients are: 21, -49, and 49.
- List the factors: 21 (1, 3, 7, 21), -49 (1, 7, 49), 49 (1, 7, 49).
- The greatest common factor for these coefficients is 7.
### 12) [tex]\(60n^4 - 80n^3 + 90n^2\)[/tex]
The coefficients are: 60, -80, and 90.
- List the factors: 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), -80 (1, 2, 4, 5, 8, 10, 20, 40, 80), 90 (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).
- The greatest common factor for these coefficients is 10.
### 13) [tex]\(36v^8 + 60v^4 - 18v\)[/tex]
The coefficients are: 36, 60, and -18.
- List the factors: 36 (1, 2, 3, 4, 6, 9, 12, 18, 36), 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), -18 (1, 2, 3, 6, 9, 18).
- The greatest common factor for these coefficients is 6.
### 14) [tex]\(-28b^4 + 49b^3 + 63b\)[/tex]
The coefficients are: -28, 49, and 63.
- List the factors: -28 (1, 2, 4, 7, 14, 28), 49 (1, 7, 49), 63 (1, 3, 7, 9, 21, 63).
- The greatest common factor for these coefficients is 7.
### 15) [tex]\(21a^2 - 7a - 21\)[/tex]
The coefficients are: 21, -7, and -21.
- List the factors: 21 (1, 3, 7, 21), -7 (1, 7), -21 (1, 3, 7, 21).
- The greatest common factor for these coefficients is 7.
### 16) [tex]\(-12x^3 - 2x + 20\)[/tex]
The coefficients are: -12, -2, and 20.
- List the factors: -12 (1, 2, 3, 4, 6, 12), -2 (1, 2), 20 (1, 2, 4, 5, 10, 20).
- The greatest common factor for these coefficients is 2.
### 17) [tex]\(-7n^2 + 56n + 42\)[/tex]
The coefficients are: -7, 56, and 42.
- List the factors: -7 (1, 7), 56 (1, 2, 4, 7, 8, 14, 28, 56), 42 (1, 2, 3, 6, 7, 14, 21, 42).
- The greatest common factor for these coefficients is 7.
### 18) [tex]\(9 - 9p^2 - 3p^5\)[/tex]
The coefficients are: 9, -9, and -3.
- List the factors: 9 (1, 3, 9), -9 (1, 3, 9), -3 (1, 3).
- The greatest common factor for these coefficients is 3.
### 19) [tex]\(30x^4 - 60x^3 - 48x^2 + 48x\)[/tex]
The coefficients are: 30, -60, -48, and 48.
- List the factors: 30 (1, 2, 3, 5, 6, 10, 15, 30), -60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), -48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48), 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48).
- The greatest common factor for these coefficients is 6.
### 20) [tex]\(6x^2 + 21x^4 + 6x^5 - 12x^4\)[/tex]
The coefficients are: 6, 21, and -12.
- List the factors: 6 (1, 2, 3, 6), 21 (1, 3, 7, 21), -12 (1, 2, 3, 4, 6, 12).
- The greatest common factor for these coefficients is 3.
These GCF values correspond to the polynomials provided.
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