Part 2/6:
The key takeaway here is that the variable ( x ) can take any value from the set of real numbers, thus making the polynomial applicable over a wide domain.
The Degree of a Polynomial
The degree of a polynomial is an important feature that indicates its highest exponent. If the leading coefficient (the coefficient of ( x^n )) is not zero, then the degree of the polynomial is simply ( n ).
For example:
If ( n = 1 ), then the polynomial is defined as ( P(x) = a_1 x + a_0 ), which represents a linear equation.
If ( n = 2 ), then it takes the form ( P(x) = a_2 x^2 + a_1 x + a_0 ), known as a quadratic equation.
If ( n = 3 ), this results in a cubic function represented by ( P(x) = a_3 x^3 + a_2 x^2 + a_1 x + a_0 ).