To determine the correct statement about the polynomial [tex]\( -8m^3 + 11m \)[/tex], we need to analyze its structure and degree. Here’s a step-by-step explanation:
1. Identifying the Number of Terms:
A polynomial can be classified based on the number of terms it has:
- A monomial has one term.
- A binomial has two terms.
- A trinomial has three terms.
Examine the polynomial [tex]\( -8m^3 + 11m \)[/tex]:
- The first term is [tex]\( -8m^3 \)[/tex].
- The second term is [tex]\( 11m \)[/tex].
Therefore, this polynomial has exactly two terms, making it a binomial.
2. Determining the Degree:
The degree of a polynomial is the highest power of the variable [tex]\( m \)[/tex] in any of its terms.
- In the term [tex]\( -8m^3 \)[/tex], the power of [tex]\( m \)[/tex] is 3.
- In the term [tex]\( 11m \)[/tex], the power of [tex]\( m \)[/tex] is 1.
The highest power among the terms is 3, making the degree of the polynomial 3.
3. Conclusion:
Based on the observations above, the polynomial [tex]\( -8m^3 + 11m \)[/tex]:
- Is a binomial (since it has two terms).
- Has a degree of 3 (since the highest power of [tex]\( m \)[/tex] is 3).
Therefore, the correct statement is:
- It is a binomial with a degree of 3.
