We appreciate your visit to Factor the greatest common factor from the polynomial tex 7x 8 y 6 7x 10 y 4 14x 6 y tex Factor completely. 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 factor the greatest common factor (GCF) from the polynomial [tex]\(7x^8y^6 + 7x^{10}y^4 + 14x^6y\)[/tex], let's follow these steps:
1. Identify the GCF of the coefficients:
The coefficients are 7, 7, and 14. The greatest common factor of these numbers is 7.
2. Identify the GCF of the [tex]\(x\)[/tex] terms:
The exponents for [tex]\(x\)[/tex] are 8, 10, and 6. The smallest exponent is 6, so the GCF for the [tex]\(x\)[/tex]-terms is [tex]\(x^6\)[/tex].
3. Identify the GCF of the [tex]\(y\)[/tex] terms:
The exponents for [tex]\(y\)[/tex] are 6, 4, and 1. The smallest exponent is 1, so the GCF for the [tex]\(y\)[/tex]-terms is [tex]\(y\)[/tex].
4. Combine the GCFs:
Combine the GCFs found above:
[tex]\[
7 \cdot x^6 \cdot y = 7x^6y
\][/tex]
5. Factor the GCF out of the polynomial:
Divide each term in the polynomial by the GCF [tex]\(7x^6y\)[/tex]:
- The first term:
[tex]\[
\frac{7x^8y^6}{7x^6y} = x^2y^5
\][/tex]
- The second term:
[tex]\[
\frac{7x^{10}y^4}{7x^6y} = x^4y^3
\][/tex]
- The third term:
[tex]\[
\frac{14x^6y}{7x^6y} = 2
\][/tex]
6. Write the factored form:
The polynomial can be written as:
[tex]\[
7x^6y(x^2y^5 + x^4y^3 + 2)
\][/tex]
So, the completely factored form of the polynomial is:
[tex]\[
7x^6y(x^2y^5 + x^4y^3 + 2)
\][/tex]
1. Identify the GCF of the coefficients:
The coefficients are 7, 7, and 14. The greatest common factor of these numbers is 7.
2. Identify the GCF of the [tex]\(x\)[/tex] terms:
The exponents for [tex]\(x\)[/tex] are 8, 10, and 6. The smallest exponent is 6, so the GCF for the [tex]\(x\)[/tex]-terms is [tex]\(x^6\)[/tex].
3. Identify the GCF of the [tex]\(y\)[/tex] terms:
The exponents for [tex]\(y\)[/tex] are 6, 4, and 1. The smallest exponent is 1, so the GCF for the [tex]\(y\)[/tex]-terms is [tex]\(y\)[/tex].
4. Combine the GCFs:
Combine the GCFs found above:
[tex]\[
7 \cdot x^6 \cdot y = 7x^6y
\][/tex]
5. Factor the GCF out of the polynomial:
Divide each term in the polynomial by the GCF [tex]\(7x^6y\)[/tex]:
- The first term:
[tex]\[
\frac{7x^8y^6}{7x^6y} = x^2y^5
\][/tex]
- The second term:
[tex]\[
\frac{7x^{10}y^4}{7x^6y} = x^4y^3
\][/tex]
- The third term:
[tex]\[
\frac{14x^6y}{7x^6y} = 2
\][/tex]
6. Write the factored form:
The polynomial can be written as:
[tex]\[
7x^6y(x^2y^5 + x^4y^3 + 2)
\][/tex]
So, the completely factored form of the polynomial is:
[tex]\[
7x^6y(x^2y^5 + x^4y^3 + 2)
\][/tex]
Thanks for taking the time to read Factor the greatest common factor from the polynomial tex 7x 8 y 6 7x 10 y 4 14x 6 y tex Factor completely. 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
