Which is true about the polynomial -8m^3 + 11m? a) It is a binomial with a degree of 2. b) It is a binomial with a degree of 3. c) It is a trinomial with a degree of 2. d) It is a trinomial with a degree of 3.
The Correct Answer and Explanation is:
The correct answer is b) It is a binomial with a degree of 3.
Explanation:
- Polynomial Structure:
A polynomial is an algebraic expression consisting of terms that are either constants or variables raised to non-negative integer exponents. In this case, the expression given is: −8m3+11m-8m^3 + 11m−8m3+11m This has two terms:- −8m3-8m^3−8m3 (term with degree 3)
- +11m+11m+11m (term with degree 1)
- Degree of the Polynomial:
The degree of a polynomial is determined by the highest degree of any term within the polynomial. In this case, the term −8m3-8m^3−8m3 has the highest exponent (3), so the degree of the entire polynomial is 3. - Review of the Options:
- a) It is a binomial with a degree of 2: Incorrect, because the degree is 3, not 2.
- b) It is a binomial with a degree of 3: Correct, because the polynomial has two terms, and the highest exponent is 3.
- c) It is a trinomial with a degree of 2: Incorrect, because it is a binomial (not a trinomial), and the degree is 3, not 2.
- d) It is a trinomial with a degree of 3: Incorrect, because it has two terms (not three), making it a binomial.
Thus, the correct answer is b) It is a binomial with a degree of 3.
