We appreciate your visit to Select the correct answer Which expression is a prime polynomial A tex x 4 20x 2 100 tex B tex x 3 27y 6 tex. 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 :
To determine which polynomial is a prime polynomial, we need to check if each expression can be factored further using integer coefficients. A prime polynomial cannot be broken down into simpler polynomials (other than by factoring out a constant).
Let's analyze each expression:
A. [tex]\(x^4 + 20x^2 - 100\)[/tex]
- This expression can be checked for factoring, but preliminary inspection shows that it can potentially be rewritten as a product of lower degree polynomials. Therefore, it's not prime.
B. [tex]\(x^3 - 27y^6\)[/tex]
- This is a difference of cubes, which can be factored using the formula:
[tex]\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)[/tex].
Here, [tex]\(a = x\)[/tex] and [tex]\(b = 3y^2\)[/tex], so it can be factored as:
[tex]\((x - 3y^2)(x^2 + 3y^2x + 9y^4)\)[/tex].
Since it can be factored, this polynomial is not prime.
C. [tex]\(3x^2 + 18y\)[/tex]
- We can factor out the greatest common factor, which is 3:
[tex]\(3(x^2 + 6y)\)[/tex].
Since it can be factored, this polynomial is not prime.
D. [tex]\(10x^4 - 5x^3 + 70x^2 + 3x\)[/tex]
- We can factor out the greatest common factor, which is x:
[tex]\(x(10x^3 - 5x^2 + 70x + 3)\)[/tex].
Since it can be factored, this polynomial is not prime.
After analyzing all the expressions, none of the provided polynomials are prime.
Let's analyze each expression:
A. [tex]\(x^4 + 20x^2 - 100\)[/tex]
- This expression can be checked for factoring, but preliminary inspection shows that it can potentially be rewritten as a product of lower degree polynomials. Therefore, it's not prime.
B. [tex]\(x^3 - 27y^6\)[/tex]
- This is a difference of cubes, which can be factored using the formula:
[tex]\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)[/tex].
Here, [tex]\(a = x\)[/tex] and [tex]\(b = 3y^2\)[/tex], so it can be factored as:
[tex]\((x - 3y^2)(x^2 + 3y^2x + 9y^4)\)[/tex].
Since it can be factored, this polynomial is not prime.
C. [tex]\(3x^2 + 18y\)[/tex]
- We can factor out the greatest common factor, which is 3:
[tex]\(3(x^2 + 6y)\)[/tex].
Since it can be factored, this polynomial is not prime.
D. [tex]\(10x^4 - 5x^3 + 70x^2 + 3x\)[/tex]
- We can factor out the greatest common factor, which is x:
[tex]\(x(10x^3 - 5x^2 + 70x + 3)\)[/tex].
Since it can be factored, this polynomial is not prime.
After analyzing all the expressions, none of the provided polynomials are prime.
Thanks for taking the time to read Select the correct answer Which expression is a prime polynomial A tex x 4 20x 2 100 tex B tex x 3 27y 6 tex. 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
