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Answer :
To determine if the expression [tex]\(-2r + 6r^5 + sr\)[/tex] is a polynomial, we need to check a few things about its terms:
1. Definition of a Polynomial:
- A polynomial is an expression made up of variables (like [tex]\(r\)[/tex]) and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
2. Examine Each Term:
- [tex]\(-2r\)[/tex]: This term is linear because it can be written as [tex]\(-2 \cdot r^1\)[/tex].
- [tex]\(6r^5\)[/tex]: This term has a degree of 5 since the exponent on [tex]\(r\)[/tex] is 5.
- [tex]\(sr\)[/tex]: This term is similar to [tex]\(-2r\)[/tex], as it is also linear ([tex]\(s \cdot r^1\)[/tex]).
3. Polynomial Verification:
- Each term has a non-negative integer exponent.
- There are no divisions by variables or other disqualifying operations.
Since all terms satisfy the criteria for a polynomial, the expression [tex]\(-2r + 6r^5 + sr\)[/tex] is indeed a polynomial.
4. Determine the Degree:
- The degree of a polynomial is determined by the term with the highest exponent. In this expression, [tex]\(6r^5\)[/tex] has the highest exponent, which is 5. Therefore, the degree of this polynomial is 5.
5. Determine the Type:
- The type of a polynomial depends on its degree:
- Degree 5 polynomials are called quintic polynomials.
Thus, the expression [tex]\(-2r + 6r^5 + sr\)[/tex] is a polynomial. It is of degree 5, and it is a quintic polynomial.
1. Definition of a Polynomial:
- A polynomial is an expression made up of variables (like [tex]\(r\)[/tex]) and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
2. Examine Each Term:
- [tex]\(-2r\)[/tex]: This term is linear because it can be written as [tex]\(-2 \cdot r^1\)[/tex].
- [tex]\(6r^5\)[/tex]: This term has a degree of 5 since the exponent on [tex]\(r\)[/tex] is 5.
- [tex]\(sr\)[/tex]: This term is similar to [tex]\(-2r\)[/tex], as it is also linear ([tex]\(s \cdot r^1\)[/tex]).
3. Polynomial Verification:
- Each term has a non-negative integer exponent.
- There are no divisions by variables or other disqualifying operations.
Since all terms satisfy the criteria for a polynomial, the expression [tex]\(-2r + 6r^5 + sr\)[/tex] is indeed a polynomial.
4. Determine the Degree:
- The degree of a polynomial is determined by the term with the highest exponent. In this expression, [tex]\(6r^5\)[/tex] has the highest exponent, which is 5. Therefore, the degree of this polynomial is 5.
5. Determine the Type:
- The type of a polynomial depends on its degree:
- Degree 5 polynomials are called quintic polynomials.
Thus, the expression [tex]\(-2r + 6r^5 + sr\)[/tex] is a polynomial. It is of degree 5, and it is a quintic polynomial.
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