Final answer:
3x^2-6x-8 is a trinomial of degree 2. a+b-c+d is a binomial of degree 1. x^3-8 is a binomial of degree 3. a^4bc^2b^2c is a monomial of degree 8. x^2yz^5 is a monomial of degree 8.
Step-by-step explanation:
The polynomial 3x^2-6x-8 is a trinomial because it has three terms. The degree of this polynomial is 2, which is determined by the highest exponent of x.
The expression a+b-c+d is a binomial because it has two terms. Since there are no variables with exponents, the degree of this polynomial is 1.
The polynomial x^3-8 is also a binomial because it has two terms. The degree of this polynomial is 3.
The expression a^4bc^2b^2c is a monomial because it has only one term. Since there are three variables with exponents, the degree of this polynomial is 8 (4+2+2).
The polynomial x^2yz^5 is also a monomial because it has only one term. The degree of this polynomial is 8 (2+1+5).