To find the number of terms and the degree of the polynomial given as [tex]\(-10w - 7\)[/tex], we will go through the problem step by step.
1. Identify the terms of the polynomial:
- A polynomial is an expression consisting of variables (such as [tex]\(w\)[/tex]) and coefficients, combined using addition, subtraction, and multiplication.
- In this polynomial, the expression is [tex]\(-10w - 7\)[/tex].
2. Count the number of terms:
- The number of terms in a polynomial is determined by counting the separate expressions connected by addition or subtraction.
- Here, we have two separate expressions: [tex]\(-10w\)[/tex] and [tex]\(-7\)[/tex]. Therefore, the total number of terms is 2.
3. Determine the degree of the polynomial:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- We examine each term:
- The term [tex]\(-10w\)[/tex] has a variable [tex]\(w\)[/tex] raised to the power of 1.
- The term [tex]\(-7\)[/tex] is a constant and can be considered as [tex]\(7w^0\)[/tex], where the power of [tex]\(w\)[/tex] is 0.
- The highest power of the variable in these terms is 1, so the degree of the polynomial is 1.
Summarizing our findings:
- Number of terms: The polynomial [tex]\(-10w - 7\)[/tex] has 2 terms.
- Degree: The degree of the polynomial [tex]\(-10w - 7\)[/tex] is 1.
Thus, the number of terms in the polynomial is 2, and the degree is 1.
