Answer :
To classify the given polynomial and determine its degree, follow these steps:
1. Identify the polynomial terms: The given polynomial is:
[tex]\[ -9 + x^4 - 5x + 2x^3 + 5x \][/tex]
2. Combine like terms, if any: In the given polynomial, the terms that have the same variable raised to the same power should be combined. Here the terms [tex]\( -5x \)[/tex] and [tex]\( 5x \)[/tex] are like terms:
[tex]\[ -9 + x^4 + 2x^3 - 5x + 5x \][/tex]
Since [tex]\( -5x \)[/tex] and [tex]\( 5x \)[/tex] cancel each other out, the polynomial simplifies to:
[tex]\[ -9 + x^4 + 2x^3 \][/tex]
3. List the terms by their degrees:
- [tex]\( x^4 \)[/tex] has a degree of 4.
- [tex]\( 2x^3 \)[/tex] has a degree of 3.
- [tex]\( -9 \)[/tex] is a constant term, which has a degree of 0.
4. Determine the highest degree: The highest degree among the terms is determined by identifying the term with the largest exponent. In this case, the term [tex]\( x^4 \)[/tex] has the highest degree, which is 4.
5. Classify the polynomial: A polynomial is classified based on its highest degree.
- Since the highest degree is 4, the polynomial is classified as a fourth-degree polynomial.
- Additionally, the polynomial is classified by the number of terms it contains. Here, after canceling out the like terms, we have:
[tex]\[ x^4, 2x^3, -9 \][/tex]
which gives us a total of three terms, classifying it as a trinomial.
Given these steps, the classification of the polynomial is as follows:
Degree: Fourth-degree polynomial
Type: Trinomial
So, the correct classification for the given polynomial is:
Fourth degree.
1. Identify the polynomial terms: The given polynomial is:
[tex]\[ -9 + x^4 - 5x + 2x^3 + 5x \][/tex]
2. Combine like terms, if any: In the given polynomial, the terms that have the same variable raised to the same power should be combined. Here the terms [tex]\( -5x \)[/tex] and [tex]\( 5x \)[/tex] are like terms:
[tex]\[ -9 + x^4 + 2x^3 - 5x + 5x \][/tex]
Since [tex]\( -5x \)[/tex] and [tex]\( 5x \)[/tex] cancel each other out, the polynomial simplifies to:
[tex]\[ -9 + x^4 + 2x^3 \][/tex]
3. List the terms by their degrees:
- [tex]\( x^4 \)[/tex] has a degree of 4.
- [tex]\( 2x^3 \)[/tex] has a degree of 3.
- [tex]\( -9 \)[/tex] is a constant term, which has a degree of 0.
4. Determine the highest degree: The highest degree among the terms is determined by identifying the term with the largest exponent. In this case, the term [tex]\( x^4 \)[/tex] has the highest degree, which is 4.
5. Classify the polynomial: A polynomial is classified based on its highest degree.
- Since the highest degree is 4, the polynomial is classified as a fourth-degree polynomial.
- Additionally, the polynomial is classified by the number of terms it contains. Here, after canceling out the like terms, we have:
[tex]\[ x^4, 2x^3, -9 \][/tex]
which gives us a total of three terms, classifying it as a trinomial.
Given these steps, the classification of the polynomial is as follows:
Degree: Fourth-degree polynomial
Type: Trinomial
So, the correct classification for the given polynomial is:
Fourth degree.
Answer:
B. fourth degree
Step-by-step explanation:
What is a degree in polynomials?
A degree is the highest power a variable in an equation has. To find the degree of a polynomial, look at the exponents!
Rewrite the expression so that the exponents are in order of highest to lowest: x⁴ +2x³ +5x-5x -9
The highest degree in this expression is 4 in x⁴
This polynomial can be classified as a fourth degree polynomial
Learn more about degrees here: https://brainly.com/question/2706981
