We appreciate your visit to Select the correct answer Which expression is a prime polynomial A tex 10x 4 5x 3 70x 2 3x tex B tex x 4 20x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Let's analyze each of the given options to determine which expression is a prime polynomial. A prime polynomial is one that cannot be factored into polynomials of lower degree with integer coefficients.
### Option A: [tex]\(10x^4 - 5x^3 + 70x^2 + 3x\)[/tex]
- Check for the greatest common factor (GCF): The GCF is [tex]\(1\)[/tex].
- It does not factor further over the integers, which might be misleading at first glance due to the combination of terms and their coefficients.
### Option B: [tex]\(x^4 + 20x^2 - 100\)[/tex]
- This expression can be factored as a difference of squares or sum/product of terms:
[tex]\[
(x^2 + 10)(x^2 - 10)
\][/tex]
- Since it can be factored, it is not a prime polynomial.
### Option C: [tex]\(3x^2 + 18y\)[/tex]
- Factor out the GCF, which is [tex]\(3\)[/tex]:
[tex]\[
3(x^2 + 6y)
\][/tex]
- Therefore, it is not prime because it can be factored.
### Option D: [tex]\(x^3 - 27y^6\)[/tex]
- This can be expressed as a difference of cubes:
[tex]\[
(x - 3y^2)(x^2 + 3xy^2 + 9y^4)
\][/tex]
- This shows that the expression can be factored and is not a prime polynomial.
After analyzing each option, it may appear that none of the expressions are prime based on the initial definition. However, generally, in such questions, the aim is to identify the least easily factorable polynomial. Since this was a misanalysis leading no option to be truly prime, seeking further instructor input or additional context would be wise.
Hence, none of the expressions meet the strict academic definition of a prime polynomial given the typical context of a classroom-style question aiming for a singular prime selection under exam conditions.
### Option A: [tex]\(10x^4 - 5x^3 + 70x^2 + 3x\)[/tex]
- Check for the greatest common factor (GCF): The GCF is [tex]\(1\)[/tex].
- It does not factor further over the integers, which might be misleading at first glance due to the combination of terms and their coefficients.
### Option B: [tex]\(x^4 + 20x^2 - 100\)[/tex]
- This expression can be factored as a difference of squares or sum/product of terms:
[tex]\[
(x^2 + 10)(x^2 - 10)
\][/tex]
- Since it can be factored, it is not a prime polynomial.
### Option C: [tex]\(3x^2 + 18y\)[/tex]
- Factor out the GCF, which is [tex]\(3\)[/tex]:
[tex]\[
3(x^2 + 6y)
\][/tex]
- Therefore, it is not prime because it can be factored.
### Option D: [tex]\(x^3 - 27y^6\)[/tex]
- This can be expressed as a difference of cubes:
[tex]\[
(x - 3y^2)(x^2 + 3xy^2 + 9y^4)
\][/tex]
- This shows that the expression can be factored and is not a prime polynomial.
After analyzing each option, it may appear that none of the expressions are prime based on the initial definition. However, generally, in such questions, the aim is to identify the least easily factorable polynomial. Since this was a misanalysis leading no option to be truly prime, seeking further instructor input or additional context would be wise.
Hence, none of the expressions meet the strict academic definition of a prime polynomial given the typical context of a classroom-style question aiming for a singular prime selection under exam conditions.
Thanks for taking the time to read Select the correct answer Which expression is a prime polynomial A tex 10x 4 5x 3 70x 2 3x tex B tex x 4 20x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
