Let's analyze the polynomial given: [tex]\(3 j^4 k - 2 j k^3 + j k^3 - 2 j^4 k + j k^3\)[/tex].
### Step-by-Step Simplification:
1. Combine Like Terms:
- Identify like terms and combine them. The polynomial consists of the terms:
[tex]\[
3 j^4 k, \quad -2 j k^3, \quad j k^3, \quad -2 j^4 k, \quad j k^3
\][/tex]
2. Group and Simplify:
- Combine the terms with [tex]\(j^4 k\)[/tex]:
[tex]\[
3 j^4 k - 2 j^4 k = (3 - 2) j^4 k = j^4 k
\][/tex]
- Combine the terms with [tex]\(j k^3\)[/tex]:
[tex]\[
-2 j k^3 + j k^3 + j k^3 = (-2 + 1 + 1) j k^3 = 0
\][/tex]
- Hence, after grouping and simplifying, we have:
[tex]\[
j^4 k
\][/tex]
3. Resulting Polynomial:
- After simplification, the polynomial reduces to:
[tex]\[
j^4 k
\][/tex]
### Determining Properties of the Simplified Polynomial:
1. Number of Terms:
- The simplified polynomial [tex]\(j^4 k\)[/tex] has exactly 1 term.
2. Degree of the Polynomial:
- The degree of a polynomial is the highest degree of its terms. Here, the term is [tex]\(j^4 k\)[/tex]. The degree is determined by adding the exponents of all variables in the term:
[tex]\[
\text{Degree} = 4 + 1 = 5
\][/tex]
Hence, the answer to the question about the simplified polynomial [tex]\(3 j^4 k - 2 j k^3 + j k^3 - 2 j^4 k + j k^3\)[/tex] is:
It has 1 term and a degree of 5.
