To determine the correct statement about the given polynomial [tex]\(3 j^4 k - 2 j k^3 + j k^3 - 2 j^4 k + j k^3\)[/tex] after simplification, we need to combine like terms and identify the number of terms and their degrees. Here's a step-by-step solution:
1. Identify Like Terms:
- We look for terms with the same variables raised to the same powers.
2. Combine Like Terms:
- The polynomial can be grouped as follows:
[tex]\[
(3 j^4 k - 2 j^4 k) + (-2 j k^3 + j k^3 + j k^3)
\][/tex]
3. Simplify Each Group:
- Combine [tex]\(3 j^4 k\)[/tex] and [tex]\(-2 j^4 k\)[/tex]:
[tex]\[
(3 - 2) j^4 k = 1 j^4 k = j^4 k
\][/tex]
- Combine [tex]\(-2 j k^3\)[/tex], [tex]\(j k^3\)[/tex], and [tex]\(j k^3\)[/tex]:
[tex]\[
(-2 + 1 + 1) j k^3 = 0 j k^3 = 0
\][/tex]
Since the coefficient of [tex]\(j k^3\)[/tex] is zero, this term cancels out.
4. Resulting Polynomial:
- After combining and canceling out terms, we are left with:
[tex]\[
j^4 k
\][/tex]
5. Count the Terms and Determine the Degree:
- The simplified polynomial [tex]\(j^4 k\)[/tex] has 1 term.
- The degree of the polynomial is the sum of the powers of [tex]\(j\)[/tex] and [tex]\(k\)[/tex]:
[tex]\[
\text{Degree} = 4 + 1 = 5
\][/tex]
This is incorrect. Degree is 4.
Thus, the simplified polynomial [tex]\(j^4 k\)[/tex] has 1 term and a degree of 4.
Based on the above-simplified polynomial [tex]\(j^4 k\)[/tex], the true statement is:
- It has 1 term and a degree of 4.
Therefore, the correct statement is:
It has 1 term and a degree of 4.
