when someone says "variables of multiple degrees"-- what does the degree of a term mean? and what are terms?

Answer 1

the power of the varable is its degree

x is 1st degree power=1
x^2 is 2nd degree power=2
and so on

Answer 2

4x^3y^5 - 6x^4 + 5x^3 + 4x^2 + x + 7

degree of a variable is the exponent
x^3 : variable x has degree 3
y^5 ; variable y has degree 5

Terms are separated by either a plus or a minus.
We have 6 terms.

Degree of a term is the sum of the exponents on the variables in the term.

The term 4x^3y^5 has degree 8 since 3 + 5 = 8.