Blake Cole
04/14/2024 · Senior High School
Which statement is true about the polynomial \( 3 j^{4} k-2 j k^{3}+j k^{3}-2 j^{4} k+j k^{3} \) after it has been fully simplified? It has 2 terms and a degree of 4 . It has 2 terms and a degree of 5 . It has 1 term and a degree of 4 . It has 1 term and a degree of 5 .
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To simplify the polynomial \( 3 j^{4} k - 2 j k^{3} + j k^{3} - 2 j^{4} k + j k^{3} \), we will combine like terms.
First, let's group the terms:
1. The terms with \( j^4 k \):
- \( 3 j^4 k - 2 j^4 k = (3 - 2) j^4 k = 1 j^4 k = j^4 k \)
2. The terms with \( j k^3 \):
- \( -2 j k^3 + j k^3 + j k^3 = (-2 + 1 + 1) j k^3 = 0 j k^3 = 0 \)
Now, combining these results, we have:
\[
j^4 k + 0 = j^4 k
\]
The simplified polynomial is \( j^4 k \).
Now, let's analyze the simplified polynomial:
- It has **1 term**.
- The degree of the polynomial is determined by the highest sum of the exponents of the variables in the term. In \( j^4 k \), the degree is \( 4 + 1 = 5 \).
Thus, the correct statement is:
**It has 1 term and a degree of 5.**
Quick Answer
It has 1 term and a degree of 5.
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