Answer :
Sure! Let's take a look at how to factor each of these expressions one by one.
6. Factor: [tex]\(6m^2 + 16m\)[/tex]
To factor this expression, first look for the greatest common factor (GCF) in both terms.
- The GCF of [tex]\(6m^2\)[/tex] and [tex]\(16m\)[/tex] is [tex]\(2m\)[/tex].
Use the GCF to factor the expression:
[tex]\[ 6m^2 + 16m = 2m(3m + 8) \][/tex]
So, the correct answer is:
A [tex]\(2m(3m + 8)\)[/tex]
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7. Factor: [tex]\(56a^3 - 8a\)[/tex]
First, find the GCF of both terms.
- The GCF of [tex]\(56a^3\)[/tex] and [tex]\(8a\)[/tex] is [tex]\(8a\)[/tex].
Use the GCF to factor the expression:
[tex]\[ 56a^3 - 8a = 8a(7a^2 - 1) \][/tex]
So, the correct answer is:
C [tex]\(8a(7a^2 - 1)\)[/tex]
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8. Factor: [tex]\(2n^2 - 8n^3\)[/tex]
Identify the GCF of both terms.
- The GCF of [tex]\(2n^2\)[/tex] and [tex]\(-8n^3\)[/tex] is [tex]\(2n^2\)[/tex].
Use the GCF to factor the expression:
[tex]\[ 2n^2 - 8n^3 = 2n^2(1 - 4n) \][/tex]
So, the correct answer is:
B [tex]\(2n^2(1 - 4n)\)[/tex]
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9. Factor: [tex]\(80x^5 - 70x^2 - 60x^7\)[/tex]
Find the GCF of all three terms.
- The GCF of the terms [tex]\(80x^5\)[/tex], [tex]\(-70x^2\)[/tex], and [tex]\(-60x^7\)[/tex] is [tex]\(10x^2\)[/tex].
Factor the expression using the GCF:
[tex]\[ 80x^5 - 70x^2 - 60x^7 = 10x^2(8x^3 - 7 - 6x^5) \][/tex]
So, the correct answer is:
C [tex]\(10x^2(8x^3 - 7 - 6x^5)\)[/tex]
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10. Factor: [tex]\(2n^3 + 16n + 12\)[/tex]
To factor this expression, check each part:
First, look for a common factor for all terms:
- The common factor for the terms [tex]\(2n^3\)[/tex], [tex]\(16n\)[/tex], and [tex]\(12\)[/tex] is [tex]\(2\)[/tex].
Factor out the 2:
[tex]\[ 2n^3 + 16n + 12 = 2(n^3 + 8n + 6) \][/tex]
So, the correct answer is:
B [tex]\(2(n^3 + 8n + 6)\)[/tex]
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11. Factor: [tex]\(10a^4 + 16a + 10a^2\)[/tex]
Find common factors in the terms.
- The GCF of [tex]\(10a^4\)[/tex], [tex]\(16a\)[/tex], and [tex]\(10a^2\)[/tex] is [tex]\(2a\)[/tex].
Factor out the GCF:
[tex]\[ 10a^4 + 16a + 10a^2 = 2a(5a^3 + 8 + 5a) \][/tex]
So, the correct answer is:
B [tex]\(2a(5a^3 + 8 + 5a)\)[/tex]
That's how you factor each of these expressions step-by-step!
6. Factor: [tex]\(6m^2 + 16m\)[/tex]
To factor this expression, first look for the greatest common factor (GCF) in both terms.
- The GCF of [tex]\(6m^2\)[/tex] and [tex]\(16m\)[/tex] is [tex]\(2m\)[/tex].
Use the GCF to factor the expression:
[tex]\[ 6m^2 + 16m = 2m(3m + 8) \][/tex]
So, the correct answer is:
A [tex]\(2m(3m + 8)\)[/tex]
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7. Factor: [tex]\(56a^3 - 8a\)[/tex]
First, find the GCF of both terms.
- The GCF of [tex]\(56a^3\)[/tex] and [tex]\(8a\)[/tex] is [tex]\(8a\)[/tex].
Use the GCF to factor the expression:
[tex]\[ 56a^3 - 8a = 8a(7a^2 - 1) \][/tex]
So, the correct answer is:
C [tex]\(8a(7a^2 - 1)\)[/tex]
---
8. Factor: [tex]\(2n^2 - 8n^3\)[/tex]
Identify the GCF of both terms.
- The GCF of [tex]\(2n^2\)[/tex] and [tex]\(-8n^3\)[/tex] is [tex]\(2n^2\)[/tex].
Use the GCF to factor the expression:
[tex]\[ 2n^2 - 8n^3 = 2n^2(1 - 4n) \][/tex]
So, the correct answer is:
B [tex]\(2n^2(1 - 4n)\)[/tex]
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9. Factor: [tex]\(80x^5 - 70x^2 - 60x^7\)[/tex]
Find the GCF of all three terms.
- The GCF of the terms [tex]\(80x^5\)[/tex], [tex]\(-70x^2\)[/tex], and [tex]\(-60x^7\)[/tex] is [tex]\(10x^2\)[/tex].
Factor the expression using the GCF:
[tex]\[ 80x^5 - 70x^2 - 60x^7 = 10x^2(8x^3 - 7 - 6x^5) \][/tex]
So, the correct answer is:
C [tex]\(10x^2(8x^3 - 7 - 6x^5)\)[/tex]
---
10. Factor: [tex]\(2n^3 + 16n + 12\)[/tex]
To factor this expression, check each part:
First, look for a common factor for all terms:
- The common factor for the terms [tex]\(2n^3\)[/tex], [tex]\(16n\)[/tex], and [tex]\(12\)[/tex] is [tex]\(2\)[/tex].
Factor out the 2:
[tex]\[ 2n^3 + 16n + 12 = 2(n^3 + 8n + 6) \][/tex]
So, the correct answer is:
B [tex]\(2(n^3 + 8n + 6)\)[/tex]
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11. Factor: [tex]\(10a^4 + 16a + 10a^2\)[/tex]
Find common factors in the terms.
- The GCF of [tex]\(10a^4\)[/tex], [tex]\(16a\)[/tex], and [tex]\(10a^2\)[/tex] is [tex]\(2a\)[/tex].
Factor out the GCF:
[tex]\[ 10a^4 + 16a + 10a^2 = 2a(5a^3 + 8 + 5a) \][/tex]
So, the correct answer is:
B [tex]\(2a(5a^3 + 8 + 5a)\)[/tex]
That's how you factor each of these expressions step-by-step!
