To determine the degree and the leading coefficient of the polynomial [tex]\( 8u^9 - 10 + 3u^7 \)[/tex], follow these steps:
1. Identify the terms of the polynomial:
The polynomial given is:
[tex]\[
8u^9 - 10 + 3u^7
\][/tex]
It consists of three terms: [tex]\(8u^9\)[/tex], [tex]\(-10\)[/tex], and [tex]\(3u^7\)[/tex].
2. Seek out the degrees of each term:
- For the term [tex]\(8u^9\)[/tex], the degree is 9.
- For the constant term [tex]\(-10\)[/tex], the degree is 0.
- For the term [tex]\(3u^7\)[/tex], the degree is 7.
3. Determine the highest degree:
Compare the degrees of all the terms. The degrees are 9, 0, and 7. The highest degree is:
[tex]\[
\boxed{9}
\][/tex]
4. Identify the leading coefficient:
The leading term is the term with the highest degree. Here, the leading term is [tex]\(8u^9\)[/tex]. The coefficient of this term is 8, so the leading coefficient is:
[tex]\[
\boxed{8}
\][/tex]
Therefore, the degree of the polynomial is [tex]\(9\)[/tex] and the leading coefficient is [tex]\(8\)[/tex].
