Question

In case of division algorithm of polynomialz, we compare the degrees. Why?

Answer 1

Because we want to express the higher degree polynomial as the product of a lower degree polynomial and sum of another polynomial.


If p(x) and g(x) are any two polynomials
with
g(x) not equal to 0, then we can find polynomials

q(x) and r(x) such that

p(x) = q(x) g(x) + r(x)

where r(x) not equal to 0 or

degree of r(x) < degree
of g(x).


The result is called Division Algorithm
for polynomials.

Dividend =
Quotient×Divisor +
Remainder

The degree of polynomial is very importance to decide g(x), q(x) and r(x).