Answer :
To identify the leading coefficient and the degree of the polynomial [tex]\(-3x^2 + 3x^6 + 4 - 7x^7 - 7x^4\)[/tex], follow these steps:
1. Understand the Degree of a Polynomial:
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the polynomial.
2. List the Terms with Their Degrees:
- [tex]\(-3x^2\)[/tex]: Degree is 2.
- [tex]\(3x^6\)[/tex]: Degree is 6.
- [tex]\(4\)[/tex]: This is a constant term with degree 0.
- [tex]\(-7x^7\)[/tex]: Degree is 7.
- [tex]\(-7x^4\)[/tex]: Degree is 4.
3. Identify the Highest Degree:
Among all the terms, the term [tex]\(-7x^7\)[/tex] has the highest degree, which is 7.
4. Determine the Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest degree. For [tex]\(-7x^7\)[/tex], the coefficient is [tex]\(-7\)[/tex].
So, the degree of the polynomial is 7, and the leading coefficient is -7.
1. Understand the Degree of a Polynomial:
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the polynomial.
2. List the Terms with Their Degrees:
- [tex]\(-3x^2\)[/tex]: Degree is 2.
- [tex]\(3x^6\)[/tex]: Degree is 6.
- [tex]\(4\)[/tex]: This is a constant term with degree 0.
- [tex]\(-7x^7\)[/tex]: Degree is 7.
- [tex]\(-7x^4\)[/tex]: Degree is 4.
3. Identify the Highest Degree:
Among all the terms, the term [tex]\(-7x^7\)[/tex] has the highest degree, which is 7.
4. Determine the Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest degree. For [tex]\(-7x^7\)[/tex], the coefficient is [tex]\(-7\)[/tex].
So, the degree of the polynomial is 7, and the leading coefficient is -7.
