At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine which of the given options is a factor in the expression
[tex]\[ 6z^4 - 4 + 9(y^3 + 3) \][/tex]
it is helpful first to recognize the algebraic structure of the expression.
Let's break down and analyze each term:
The expression is:
[tex]\[ 6z^4 - 4 + 9(y^3 + 3) \][/tex]
Firstly, let's re-write the expression to make it more clear:
[tex]\[ 6z^4 - 4 + 9y^3 + 27 \][/tex]
Now, let’s check each of the given options to determine if they are factors within this expression:
Option A: [tex]\(-4 + 9(y^3 + 3)\)[/tex]
[tex]\[ -4 + 9(y^3 + 3) \][/tex]
Simplifies to:
[tex]\[ -4 + 9y^3 + 27 \][/tex]
Which results in:
[tex]\[ 9y^3 + 23 \][/tex]
Clearly, this does not match any part of the original expression.
Option B: [tex]\(6z^4 - 4\)[/tex]
This term, [tex]\(6z^4 - 4\)[/tex], appears entirely independent of the term [tex]\(9(y^3 + 3)\)[/tex].
However, just because it is present in the original expression does not imply [tex]\(6z^4 - 4\)[/tex] is a factor. In the original expression, they are separate addends and thus not nested factors.
Option C: [tex]\(9(y^3 + 3)\)[/tex]
For this, factor out [tex]\(9(y^3 + 3)\)[/tex]:
[tex]\[ 9(y^3 + 3) = 9y^3 + 27 \][/tex]
This matches the part of the expression [tex]\(9y^3 + 27\)[/tex].
Option D: [tex]\((y^3 + 3)\)[/tex]
Here we can factor out [tex]\(y^3 + 3\)[/tex] from [tex]\(9(y^3 + 3)\)[/tex]:
[tex]\[ 9(y^3 + 3) = 9y^3 + 27 \][/tex]
As seen, [tex]\(y^3 + 3\)[/tex] indeed is nested as part of [tex]\(9(y^3 + 3)\)[/tex].
After considering each option, we observe:
- Options C and D correctly identify parts of the expression components as factors.
- Bearing in mind, the simplest form of the factor present within another nested factor fits our questions’ criteria.
Therefore, the best answer among the given choices that directly factors into the original expression is:
[tex]\[ D. \left(y^3 + 3\right) \][/tex]
[tex]\[ 6z^4 - 4 + 9(y^3 + 3) \][/tex]
it is helpful first to recognize the algebraic structure of the expression.
Let's break down and analyze each term:
The expression is:
[tex]\[ 6z^4 - 4 + 9(y^3 + 3) \][/tex]
Firstly, let's re-write the expression to make it more clear:
[tex]\[ 6z^4 - 4 + 9y^3 + 27 \][/tex]
Now, let’s check each of the given options to determine if they are factors within this expression:
Option A: [tex]\(-4 + 9(y^3 + 3)\)[/tex]
[tex]\[ -4 + 9(y^3 + 3) \][/tex]
Simplifies to:
[tex]\[ -4 + 9y^3 + 27 \][/tex]
Which results in:
[tex]\[ 9y^3 + 23 \][/tex]
Clearly, this does not match any part of the original expression.
Option B: [tex]\(6z^4 - 4\)[/tex]
This term, [tex]\(6z^4 - 4\)[/tex], appears entirely independent of the term [tex]\(9(y^3 + 3)\)[/tex].
However, just because it is present in the original expression does not imply [tex]\(6z^4 - 4\)[/tex] is a factor. In the original expression, they are separate addends and thus not nested factors.
Option C: [tex]\(9(y^3 + 3)\)[/tex]
For this, factor out [tex]\(9(y^3 + 3)\)[/tex]:
[tex]\[ 9(y^3 + 3) = 9y^3 + 27 \][/tex]
This matches the part of the expression [tex]\(9y^3 + 27\)[/tex].
Option D: [tex]\((y^3 + 3)\)[/tex]
Here we can factor out [tex]\(y^3 + 3\)[/tex] from [tex]\(9(y^3 + 3)\)[/tex]:
[tex]\[ 9(y^3 + 3) = 9y^3 + 27 \][/tex]
As seen, [tex]\(y^3 + 3\)[/tex] indeed is nested as part of [tex]\(9(y^3 + 3)\)[/tex].
After considering each option, we observe:
- Options C and D correctly identify parts of the expression components as factors.
- Bearing in mind, the simplest form of the factor present within another nested factor fits our questions’ criteria.
Therefore, the best answer among the given choices that directly factors into the original expression is:
[tex]\[ D. \left(y^3 + 3\right) \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.