To find the leading coefficient and the degree of the polynomial [tex]\(18u + 2 - u^9 - 10u^7\)[/tex], follow these steps:
1. Identify the terms in the polynomial:
- [tex]\(18u\)[/tex]
- [tex]\(2\)[/tex]
- [tex]\(-u^9\)[/tex]
- [tex]\(-10u^7\)[/tex]
2. Determine the degree of each term:
- The term [tex]\(18u\)[/tex] has a degree of [tex]\(1\)[/tex].
- The term [tex]\(2\)[/tex] has a degree of [tex]\(0\)[/tex].
- The term [tex]\(-u^9\)[/tex] has a degree of [tex]\(9\)[/tex].
- The term [tex]\(-10u^7\)[/tex] has a degree of [tex]\(7\)[/tex].
3. Find the term with the highest degree:
- Among the terms, the highest degree is [tex]\(9\)[/tex], which comes from the term [tex]\(-u^9\)[/tex].
4. Identify the degree of the polynomial:
- The degree of the polynomial is the highest degree of its terms, which is [tex]\(9\)[/tex].
5. Determine the leading term:
- The term with the highest power of [tex]\(u\)[/tex] is the leading term. In this polynomial, the leading term is [tex]\(-u^9\)[/tex].
6. Extract the leading coefficient:
- The leading coefficient is the coefficient of the leading term. For the leading term [tex]\(-u^9\)[/tex], the coefficient is [tex]\(-1\)[/tex].
Putting it all together:
- The degree of the polynomial [tex]\(18u + 2 - u^9 - 10u^7\)[/tex] is [tex]\(9\)[/tex].
- The leading coefficient of the polynomial is [tex]\(-1\)[/tex].
Thus, the degree of the polynomial is [tex]\(9\)[/tex] and the leading coefficient is [tex]\(-1\)[/tex].
