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Answer :
Sure! Let's go through each expression step-by-step to factor them.
Expression 13: [tex]\(-3k^3 + 15k^2 - 6k\)[/tex]
1. Look for the greatest common factor (GCF): The GCF here is [tex]\(-3k\)[/tex].
2. Factor out the GCF:
[tex]\[
-3k(k^2 - 5k + 2)
\][/tex]
Expression 14: [tex]\(50p^3 + 50p^2 - 20\)[/tex]
1. Identify the GCF: The GCF is [tex]\(10\)[/tex].
2. Factor out the GCF:
[tex]\[
10(5p^3 + 5p^2 - 2)
\][/tex]
Expression 15: [tex]\(32n^3 + 28n - 20\)[/tex]
1. Find the GCF, which is [tex]\(4\)[/tex].
2. Factor out the GCF:
[tex]\[
4(8n^3 + 7n - 5)
\][/tex]
Expression 16: [tex]\(-90x^5 + 100x + 60\)[/tex]
1. Identify the GCF: The GCF is [tex]\(-10\)[/tex].
2. Factor out the GCF:
[tex]\[
-10(9x^5 - 10x - 6)
\][/tex]
Expression 17: [tex]\(3m^2 + 9m + 27\)[/tex]
1. Find the GCF, which is [tex]\(3\)[/tex].
2. Factor out the GCF:
[tex]\[
3(m^2 + 3m + 9)
\][/tex]
Expression 18: [tex]\(12r^2 + 4r - 12\)[/tex]
1. The GCF here is [tex]\(4\)[/tex].
2. Factor out the GCF:
[tex]\[
4(3r^2 + r - 3)
\][/tex]
Expression 19: [tex]\(64 + 40x^2 + 72x\)[/tex]
1. Identify the GCF: The GCF is [tex]\(8\)[/tex].
2. Factor out the GCF:
[tex]\[
8(5x^2 + 9x + 8)
\][/tex]
Expression 20: [tex]\(-18n^2 + 15n - 15\)[/tex]
1. The GCF is [tex]\(-3\)[/tex].
2. Factor out the GCF:
[tex]\[
-3(6n^2 - 5n + 5)
\][/tex]
These steps show how each expression is factored using the greatest common factor technique. Factoring helps simplify the expressions and can make solving equations or analyzing polynomials easier.
Expression 13: [tex]\(-3k^3 + 15k^2 - 6k\)[/tex]
1. Look for the greatest common factor (GCF): The GCF here is [tex]\(-3k\)[/tex].
2. Factor out the GCF:
[tex]\[
-3k(k^2 - 5k + 2)
\][/tex]
Expression 14: [tex]\(50p^3 + 50p^2 - 20\)[/tex]
1. Identify the GCF: The GCF is [tex]\(10\)[/tex].
2. Factor out the GCF:
[tex]\[
10(5p^3 + 5p^2 - 2)
\][/tex]
Expression 15: [tex]\(32n^3 + 28n - 20\)[/tex]
1. Find the GCF, which is [tex]\(4\)[/tex].
2. Factor out the GCF:
[tex]\[
4(8n^3 + 7n - 5)
\][/tex]
Expression 16: [tex]\(-90x^5 + 100x + 60\)[/tex]
1. Identify the GCF: The GCF is [tex]\(-10\)[/tex].
2. Factor out the GCF:
[tex]\[
-10(9x^5 - 10x - 6)
\][/tex]
Expression 17: [tex]\(3m^2 + 9m + 27\)[/tex]
1. Find the GCF, which is [tex]\(3\)[/tex].
2. Factor out the GCF:
[tex]\[
3(m^2 + 3m + 9)
\][/tex]
Expression 18: [tex]\(12r^2 + 4r - 12\)[/tex]
1. The GCF here is [tex]\(4\)[/tex].
2. Factor out the GCF:
[tex]\[
4(3r^2 + r - 3)
\][/tex]
Expression 19: [tex]\(64 + 40x^2 + 72x\)[/tex]
1. Identify the GCF: The GCF is [tex]\(8\)[/tex].
2. Factor out the GCF:
[tex]\[
8(5x^2 + 9x + 8)
\][/tex]
Expression 20: [tex]\(-18n^2 + 15n - 15\)[/tex]
1. The GCF is [tex]\(-3\)[/tex].
2. Factor out the GCF:
[tex]\[
-3(6n^2 - 5n + 5)
\][/tex]
These steps show how each expression is factored using the greatest common factor technique. Factoring helps simplify the expressions and can make solving equations or analyzing polynomials easier.
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