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Answer :
Sure! Let's work through factoring each expression by finding the Greatest Common Factor (GCF) and factoring it out.
### 11) [tex]\(20 - 35n^2 - 20n^3\)[/tex]
1. Identify the GCF of the coefficients (20, 35, and 20), which is 5.
2. There is also a common factor of [tex]\(n\)[/tex] in the terms with [tex]\(n\)[/tex].
3. Factor out the GCF, which is 5:
[tex]\[ 5(4 - 7n^2 - 4n^3) \][/tex]
### 12) [tex]\(9x^6 - 63x^3 - 90x^2\)[/tex]
1. Identify the GCF of the coefficients (9, 63, and 90), which is 9.
2. The smallest power of [tex]\(x\)[/tex] common in all terms is [tex]\(x^2\)[/tex].
3. Factor out the GCF, which is [tex]\(9x^2\)[/tex]:
[tex]\[ 9x^2(x^4 - 7x - 10) \][/tex]
### 13) [tex]\(-3k^3 + 15k^2 - 6k\)[/tex]
1. Identify the GCF of the coefficients (-3, 15, and -6), which is 3. We usually factor out the negative sign when the first term is negative, so we'll factor out -3.
2. The smallest power of [tex]\(k\)[/tex] common in all terms is [tex]\(k\)[/tex].
3. Factor out the GCF, which is [tex]\(-3k\)[/tex]:
[tex]\[ -3k(k^2 - 5k + 2) \][/tex]
### 14) [tex]\(50p^3 + 50p^2 - 20\)[/tex]
1. Identify the GCF of the coefficients (50, 50, and 20), which is 10.
2. The smallest power of [tex]\(p\)[/tex] common in terms [tex]\(p^2\)[/tex] and [tex]\(p^3\)[/tex] is [tex]\(p^2\)[/tex], but since not all terms have [tex]\(p\)[/tex], we're just factoring out 10.
3. Factor out the GCF, which is 10:
[tex]\[ 10(5p^3 + 5p^2 - 2) \][/tex]
### 15) [tex]\(32n^3 + 28n - 20\)[/tex]
1. Identify the GCF of the coefficients (32, 28, and 20), which is 4.
2. Factor out the GCF, which is 4:
[tex]\[ 4(8n^3 + 7n - 5) \][/tex]
### 16) [tex]\(-90x^5 + 100x + 60\)[/tex]
1. Identify the GCF of the coefficients (-90, 100, and 60), which is 10. Again, we usually factor out the negative sign when the first coefficient is negative, so we'll factor out -10.
2. Factor out the GCF, which is [tex]\(-10\)[/tex]:
[tex]\[ -10(9x^5 - 10x - 6) \][/tex]
That's how you factor each expression by the GCF. Make sure to write down the factored form as part of your work. If you have any more questions, feel free to ask!
### 11) [tex]\(20 - 35n^2 - 20n^3\)[/tex]
1. Identify the GCF of the coefficients (20, 35, and 20), which is 5.
2. There is also a common factor of [tex]\(n\)[/tex] in the terms with [tex]\(n\)[/tex].
3. Factor out the GCF, which is 5:
[tex]\[ 5(4 - 7n^2 - 4n^3) \][/tex]
### 12) [tex]\(9x^6 - 63x^3 - 90x^2\)[/tex]
1. Identify the GCF of the coefficients (9, 63, and 90), which is 9.
2. The smallest power of [tex]\(x\)[/tex] common in all terms is [tex]\(x^2\)[/tex].
3. Factor out the GCF, which is [tex]\(9x^2\)[/tex]:
[tex]\[ 9x^2(x^4 - 7x - 10) \][/tex]
### 13) [tex]\(-3k^3 + 15k^2 - 6k\)[/tex]
1. Identify the GCF of the coefficients (-3, 15, and -6), which is 3. We usually factor out the negative sign when the first term is negative, so we'll factor out -3.
2. The smallest power of [tex]\(k\)[/tex] common in all terms is [tex]\(k\)[/tex].
3. Factor out the GCF, which is [tex]\(-3k\)[/tex]:
[tex]\[ -3k(k^2 - 5k + 2) \][/tex]
### 14) [tex]\(50p^3 + 50p^2 - 20\)[/tex]
1. Identify the GCF of the coefficients (50, 50, and 20), which is 10.
2. The smallest power of [tex]\(p\)[/tex] common in terms [tex]\(p^2\)[/tex] and [tex]\(p^3\)[/tex] is [tex]\(p^2\)[/tex], but since not all terms have [tex]\(p\)[/tex], we're just factoring out 10.
3. Factor out the GCF, which is 10:
[tex]\[ 10(5p^3 + 5p^2 - 2) \][/tex]
### 15) [tex]\(32n^3 + 28n - 20\)[/tex]
1. Identify the GCF of the coefficients (32, 28, and 20), which is 4.
2. Factor out the GCF, which is 4:
[tex]\[ 4(8n^3 + 7n - 5) \][/tex]
### 16) [tex]\(-90x^5 + 100x + 60\)[/tex]
1. Identify the GCF of the coefficients (-90, 100, and 60), which is 10. Again, we usually factor out the negative sign when the first coefficient is negative, so we'll factor out -10.
2. Factor out the GCF, which is [tex]\(-10\)[/tex]:
[tex]\[ -10(9x^5 - 10x - 6) \][/tex]
That's how you factor each expression by the GCF. Make sure to write down the factored form as part of your work. If you have any more questions, feel free to ask!
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