Okay I don't know how much you already know so I will just try and explain everything. For the first set of problems it says to determine if its a polynomial and what type of polynomial and its degree. A term are things like x, y, xy, x^2, xy^2, 4xy^3, etc. The way I remember is that if the variables or numbers are MULTIPLYING or DIVIDING then it is a term. A polynomial is any expression with multiple terms such as x + y or 4xy^2 + 5z^3 - 4q so it is the ADDITION or SUBTRACTION of terms. Do you follow so far?
Okay next part asks about the degree. The degree of an expression is the highest exponent in the expression. So the degree of x would be 1 and the degree of x^2 + 4y^8 would be 8 since 8 is the highest exponent.
Now it asks about what type of polynomial it is. Monomial means there is ONE term. Binomial means there are TWO terms, Trinomial means THREE, and so on.
Okay now once you solved all of those first problems it asks to write in standard form. Standard form for polynomials are the terms in descending degree order, meaning the term with the highest exponent goes first and then decreases from there. The leading coefficient is just the coefficient of the term of the highest degree EX: 5x^2 + 2x^3 + y in standard form would be 2x^3 + 5x^2 + y and the leading coefficient would be 2
Now the final set is just simplification of the polynomials. What you need to do is combine like terms. With addition it is pretty straight forward, however with subtraction many students mess up. What I suggest to do with subtraction is distribute the negative sign over the polynomial. If you are not sure what this means just ask and I'll try to comment.
