Let's start with classifications:
monomial: there's only one term, so not + or -
examples: [tex]7x^5[/tex] or [tex]-9x[/tex]
binomial: there are two terms, so only one + or one -
examples: [tex]7x^5 - 9x[/tex] or [tex]-3x^2+1[/tex]
trinomial: there are three terms
examples: [tex]7x^5 - 9x^4 + 3[/tex] or [tex]-8p^3+2x^2-x[/tex]
Now the degree of a term is the number of variables multplied on that term.
example: [tex]7x^3[/tex] is degee three, because[tex]7x^3 = 7\cdot x\cdot x\cdot x[/tex] and there are three x's.
example: [tex]-8x^2[/tex] really means [tex]-8\cdot x\cdot x[/tex], so that's degree 2.
Finally, the degree of a polynomial (which is what this is asking for) is the degree of the highest degree term.
example: [tex]7x^5 - 9x[/tex] has a 5th degree term and 1st degree term, so this is a degree 5 polynomial, since that's the greatest.
