Let's classify each polynomial and state its degree:

a) $-4a^6bc^2$

• Classification: This is a monomial, since it consists of a single term.

• Degree: The degree of a monomial is the sum of the exponents of its variables. In this case:

  • $a^6$ has an exponent of 6,
  • $b$ has an exponent of 1 (implied),
  • $c^2$ has an exponent of 2.
  • Sum: $6 + 1 + 2 = 9$.

  Degree: 9.

b) $2p^3q^2 + 3p^4q$

• Classification: This is a binomial, since it consists of two terms.

• Degree: For each term, the degree is the sum of the exponents of the variables:

  • For the first term $2p^3q^2$, the degree is:
    • $p^3$ has an exponent of 3,
    • $q^2$ has an exponent of 2.
    • Sum: $3 + 2 = 5$.
  • For the second term $3p^4q$, the degree is:
    • $p^4$ has an exponent of 4,
    • $q$ has an exponent of 1 (implied).
    • Sum: $4 + 1 = 5$.

  Since both terms have a degree of 5, the degree of the binomial is 5 (the highest degree term).

---

Would you like more details or have any questions about the classifications or degrees?

Related Questions:

1. What is the difference between a monomial, binomial, and trinomial?
2. How do you find the degree of a polynomial with multiple variables?
3. What happens if a polynomial has no exponents on certain variables?
4. How would the classification change if a polynomial had three terms instead of two?
5. How do coefficients affect the classification or degree of a polynomial?

Tip: The degree of a polynomial is always determined by the term with the highest sum of exponents.