State division algorithm for polynomials.

The division algorithm for polynomials states that given two polynomials, say f(x) and g(x), where g(x) is not the zero polynomial, there exist unique polynomials q(x) (the quotient) and r(x) (the remainder) such that:

f(x) = g(x) * q(x) + r(x)

Here:

f(x) is the dividend (the polynomial to be divided),
g(x) is the divisor (the polynomial you are dividing by),
q(x) is the quotient (the result of the division),
r(x) is the remainder (which will have a degree strictly less than the degree of g(x)).
The degree of the remainder r(x) is always less than the degree of the divisor g(x). If the remainder is zero, it means f(x) is exactly divisible by g(x).

In summary, the division algorithm for polynomials expresses any polynomial division as:

f(x) = g(x) * q(x) + r(x), where the degree of r(x) < the degree of g(x).