Answer :
Let's analyze the polynomial [tex]\( 3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3 \)[/tex] and simplify it step by step.
### Combining Like Terms
First, identify and combine like terms in the polynomial. The original polynomial can be broken down into terms involving [tex]\( j^4k \)[/tex] and [tex]\( jk^3 \)[/tex]:
[tex]\[ 3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3 \][/tex]
1. Combine the [tex]\( j^4k \)[/tex] terms:
[tex]\[ 3j^4k - 2j^4k = j^4k \][/tex]
2. Combine the [tex]\( jk^3 \)[/tex] terms:
[tex]\[ -2jk^3 + jk^3 + jk^3 = 0jk^3 = 0 \][/tex]
After combining the like terms, the polynomial simplifies to:
[tex]\[ j^4k \][/tex]
### Degree of the Polynomial
The degree of a polynomial is the highest sum of the exponents in any single term. For the term [tex]\( j^4k \)[/tex]:
[tex]\[ \text{Degree} = 4 (from \, j^4) + 1 (from \, k) = 5 \][/tex]
### Number of Terms
After simplification, there is only one term in the polynomial:
[tex]\[ j^4k \][/tex]
### Conclusion
The simplified polynomial [tex]\( j^4k \)[/tex] has:
- 1 term
- A degree of 5
Thus, the correct statement is:
It has 1 term and a degree of 5.
### Combining Like Terms
First, identify and combine like terms in the polynomial. The original polynomial can be broken down into terms involving [tex]\( j^4k \)[/tex] and [tex]\( jk^3 \)[/tex]:
[tex]\[ 3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3 \][/tex]
1. Combine the [tex]\( j^4k \)[/tex] terms:
[tex]\[ 3j^4k - 2j^4k = j^4k \][/tex]
2. Combine the [tex]\( jk^3 \)[/tex] terms:
[tex]\[ -2jk^3 + jk^3 + jk^3 = 0jk^3 = 0 \][/tex]
After combining the like terms, the polynomial simplifies to:
[tex]\[ j^4k \][/tex]
### Degree of the Polynomial
The degree of a polynomial is the highest sum of the exponents in any single term. For the term [tex]\( j^4k \)[/tex]:
[tex]\[ \text{Degree} = 4 (from \, j^4) + 1 (from \, k) = 5 \][/tex]
### Number of Terms
After simplification, there is only one term in the polynomial:
[tex]\[ j^4k \][/tex]
### Conclusion
The simplified polynomial [tex]\( j^4k \)[/tex] has:
- 1 term
- A degree of 5
Thus, the correct statement is:
It has 1 term and a degree of 5.
