Polynomials are functions or expressions that can be evaluated in a finite number of additions, multiplications, and subtractions. However, they require no division for their evaluation. (Fractions are considered constants in this context). Polynomials have a whole language associated with them that you need to understand. You also need to be able to manipulate polynomial expressions to obtain their standard form.
Consider the polynomial $$p(x) = (x^2+1)(x-2)-3x-1.$$
Its degree is and its leading coefficient is .
In standard form it can be written as
$p(x) =$ $x^3$ $+$ $x^2$ $+$ $x$ $+$ .
Note that some of these answers may be negative.