Question: Name the polynomial by degree, number of terms, and the coefficient where degree was found.
$$2x^2y^2 + 3xy - 4y^3$$
Select the correct response:
Degree: 3
Number of terms: 4
Name: Trinomial
Leading coefficient: 4
1. **State the problem:** We are given the polynomial $$2x^2y^2 + 3xy - 4y^3$$ and need to identify its degree, number of terms, name, and leading coefficient.
2. **Number of terms:** Count the terms separated by plus or minus signs.
Terms: $$2x^2y^2$$, $$3xy$$, $$-4y^3$$
Number of terms = 3.
3. **Degree of the polynomial:** The degree is the highest sum of exponents in any term.
- For $$2x^2y^2$$, degree = $$2 + 2 = 4$$
- For $$3xy$$, degree = $$1 + 1 = 2$$
- For $$-4y^3$$, degree = $$3$$
Highest degree = $$4$$.
4. **Name of the polynomial by number of terms:**
- 1 term: Monomial
- 2 terms: Binomial
- 3 terms: Trinomial
Here, number of terms = 3, so it is a Trinomial.
5. **Leading coefficient:** The leading term is the term with the highest degree, which is $$2x^2y^2$$.
Leading coefficient = $$2$$.
6. **Summary:**
- Degree: $$4$$
- Number of terms: $$3$$
- Name: Trinomial
- Leading coefficient: $$2$$
**Final answer:** Degree is 4, number of terms is 3, name is Trinomial, leading coefficient is 2.