Answer :
To find the degree of the polynomial [tex]\(4x + 8x^3 - 10 - 2x^7 + 9x^4\)[/tex], you need to identify the highest power of the variable [tex]\(x\)[/tex] present in the expression.
Here's how to do it step-by-step:
1. Identify the terms: The polynomial is made up of several terms, which are:
- [tex]\(4x\)[/tex]
- [tex]\(8x^3\)[/tex]
- [tex]\(-10\)[/tex]
- [tex]\(-2x^7\)[/tex]
- [tex]\(9x^4\)[/tex]
2. Determine the degree of each term:
- [tex]\(4x\)[/tex] has a degree of 1 because the exponent of [tex]\(x\)[/tex] is 1.
- [tex]\(8x^3\)[/tex] has a degree of 3 because the exponent of [tex]\(x\)[/tex] is 3.
- [tex]\(-10\)[/tex] is a constant term and has a degree of 0 (as there is no [tex]\(x\)[/tex]).
- [tex]\(-2x^7\)[/tex] has a degree of 7 because the exponent of [tex]\(x\)[/tex] is 7.
- [tex]\(9x^4\)[/tex] has a degree of 4 because the exponent of [tex]\(x\)[/tex] is 4.
3. Identify the highest degree: The degree of the polynomial is determined by the term with the highest exponent. In this polynomial, the term with the highest exponent is [tex]\(-2x^7\)[/tex], which has an exponent of 7.
Therefore, the degree of the polynomial [tex]\(4x + 8x^3 - 10 - 2x^7 + 9x^4\)[/tex] is 7.
Here's how to do it step-by-step:
1. Identify the terms: The polynomial is made up of several terms, which are:
- [tex]\(4x\)[/tex]
- [tex]\(8x^3\)[/tex]
- [tex]\(-10\)[/tex]
- [tex]\(-2x^7\)[/tex]
- [tex]\(9x^4\)[/tex]
2. Determine the degree of each term:
- [tex]\(4x\)[/tex] has a degree of 1 because the exponent of [tex]\(x\)[/tex] is 1.
- [tex]\(8x^3\)[/tex] has a degree of 3 because the exponent of [tex]\(x\)[/tex] is 3.
- [tex]\(-10\)[/tex] is a constant term and has a degree of 0 (as there is no [tex]\(x\)[/tex]).
- [tex]\(-2x^7\)[/tex] has a degree of 7 because the exponent of [tex]\(x\)[/tex] is 7.
- [tex]\(9x^4\)[/tex] has a degree of 4 because the exponent of [tex]\(x\)[/tex] is 4.
3. Identify the highest degree: The degree of the polynomial is determined by the term with the highest exponent. In this polynomial, the term with the highest exponent is [tex]\(-2x^7\)[/tex], which has an exponent of 7.
Therefore, the degree of the polynomial [tex]\(4x + 8x^3 - 10 - 2x^7 + 9x^4\)[/tex] is 7.
