To identify the degree of each term of the polynomial [tex]\(4x^2 - 7x + 8\)[/tex] and the overall degree of the polynomial, follow these steps:
1. Identify the degree of each term:
- The first term is [tex]\(4x^2\)[/tex]:
- The coefficient is 4.
- The exponent (degree) of [tex]\(x\)[/tex] in this term is 2.
- Thus, the degree of the first term is [tex]\(\boxed{2}\)[/tex].
- The second term is [tex]\(-7x\)[/tex]:
- The coefficient is -7.
- The exponent (degree) of [tex]\(x\)[/tex] in this term is 1.
- Thus, the degree of the second term is [tex]\(\boxed{1}\)[/tex].
- The third term is 8:
- The coefficient is 8.
- There is no [tex]\(x\)[/tex] term, which means the exponent (degree) of [tex]\(x\)[/tex] is 0.
- Thus, the degree of the third term is [tex]\(\boxed{0}\)[/tex].
2. Identify the degree of the polynomial:
- The degree of a polynomial is determined by the highest degree of its individual terms.
- Among the degrees of the terms, which are 2, 1, and 0, the highest degree is 2.
Therefore, the degree of the polynomial is [tex]\(\boxed{2}\)[/tex].
To summarize:
The degree of the first term is [tex]\(\boxed{2}\)[/tex].
The degree of the second term is [tex]\(\boxed{1}\)[/tex].
The degree of the third term is [tex]\(\boxed{0}\)[/tex].
The degree of the polynomial is [tex]\(\boxed{2}\)[/tex].
