What are the degree and leading coefficient of the polynomial?

[tex]\[ 8u^9 - 10 + 3u^7 \][/tex]

Degree: [tex]\(\square\)[/tex]

Leading coefficient: [tex]\(\square\)[/tex]



Answer :

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].