We appreciate your visit to Express the solution in standard form then classify the resulting polynomial by its degree and number of terms tex left 9x 6 7x 5 16. 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 solve the given polynomial expression and classify the result, follow these steps:
1. Identify the Polynomial Expressions:
We start with two polynomials:
[tex]\[
(-9x^6 - 7x^5 - 16) + (3x^6 - 7x^5 + 14)
\][/tex]
2. Combine Like Terms:
- For the [tex]\(x^6\)[/tex] terms, combine [tex]\(-9x^6\)[/tex] and [tex]\(3x^6\)[/tex]:
[tex]\[
-9x^6 + 3x^6 = -6x^6
\][/tex]
- For the [tex]\(x^5\)[/tex] terms, combine [tex]\(-7x^5\)[/tex] and [tex]\(-7x^5\)[/tex]:
[tex]\[
-7x^5 - 7x^5 = -14x^5
\][/tex]
- For the constant terms, combine [tex]\(-16\)[/tex] and [tex]\(14\)[/tex]:
[tex]\[
-16 + 14 = -2
\][/tex]
3. Write the Simplified Polynomial in Standard Form:
Arrange the combined terms in order of decreasing degree:
[tex]\[
-6x^6 - 14x^5 - 2
\][/tex]
4. Classify the Polynomial:
- Degree: The highest power of [tex]\(x\)[/tex] in the polynomial is 6, so the degree is 6.
- Number of Terms: There are three terms in the polynomial: [tex]\(-6x^6\)[/tex], [tex]\(-14x^5\)[/tex], and [tex]\(-2\)[/tex].
In conclusion, the simplified polynomial is [tex]\(-6x^6 - 14x^5 - 2\)[/tex], classified as a sixth-degree polynomial with three terms.
1. Identify the Polynomial Expressions:
We start with two polynomials:
[tex]\[
(-9x^6 - 7x^5 - 16) + (3x^6 - 7x^5 + 14)
\][/tex]
2. Combine Like Terms:
- For the [tex]\(x^6\)[/tex] terms, combine [tex]\(-9x^6\)[/tex] and [tex]\(3x^6\)[/tex]:
[tex]\[
-9x^6 + 3x^6 = -6x^6
\][/tex]
- For the [tex]\(x^5\)[/tex] terms, combine [tex]\(-7x^5\)[/tex] and [tex]\(-7x^5\)[/tex]:
[tex]\[
-7x^5 - 7x^5 = -14x^5
\][/tex]
- For the constant terms, combine [tex]\(-16\)[/tex] and [tex]\(14\)[/tex]:
[tex]\[
-16 + 14 = -2
\][/tex]
3. Write the Simplified Polynomial in Standard Form:
Arrange the combined terms in order of decreasing degree:
[tex]\[
-6x^6 - 14x^5 - 2
\][/tex]
4. Classify the Polynomial:
- Degree: The highest power of [tex]\(x\)[/tex] in the polynomial is 6, so the degree is 6.
- Number of Terms: There are three terms in the polynomial: [tex]\(-6x^6\)[/tex], [tex]\(-14x^5\)[/tex], and [tex]\(-2\)[/tex].
In conclusion, the simplified polynomial is [tex]\(-6x^6 - 14x^5 - 2\)[/tex], classified as a sixth-degree polynomial with three terms.
Thanks for taking the time to read Express the solution in standard form then classify the resulting polynomial by its degree and number of terms tex left 9x 6 7x 5 16. 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
