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State division algorithm for polynomials.
The polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree; it is a generalized version of the familiar arithmetic technique called long division. It can be done manually because it separates a complex division problem into smaller ones.
Let’s take the Example:
f(x) and g(x) are two polynomials with,
g(x)≠0,
Now we can find the polynomials p(x) and q(x) such that,
f(x) = p(x) × g(x) × q(x)
Where q(x) = 0 or degree of q(x) < is degree of g(x).
The result is;
Dividend = Quotient × Divisor + Remainder
This is known as the Division Algorithm for polynomials.