A polynomial is string of variables and numbers. They are linked together with addition and subtraction. The individual terms are multiplied together. An example is 3b + 2a, where the 3b is 3*b (it is shorthand in a way) and the 2a is 2*a. An addition sign connects them both. Another example is b + 2b – 9 in which b is just a term that is squared or multiplied and the 2b is just 2 * b subtracted by 9. Any algebraic expression with more than 3 terms do not have a special name and are called polynomials.
The advice I would give to the students of the future is to try to avoid polynomials because they are very dangerous. But if they cannot be avoided try to combine like terms, like 2b and 3b would make 5b.