Hey vjnr.

Basically a polynomial is a function that takes an input x and produces an output y where for each x we get:

y(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_0 where a_i's are just constant real numbers and n is a positive whole number (greater than 0).

We can plot the function by calculating y(x) for a lot of different values of x and then by plotting the points either on graph paper or on a computer screen.

The constant term is the a_0 term, the degree is the value of n, and monomials have a_n = not zero and the rest equal to zero.