Question

if p(x) and g(x) are any two polynomials with g(x) cannot be equal to 0,then we can find polynomials q(x) and r(x) such that p(x)=g(x)*p(x)+r(x) where r(x)=0 or degree of r(x)

Answer 1

Your question states p(x)/g(x) gives
quotient as o.That means g(x) *0=p
(x).This is possible only if P(x) is 0 and
g(x) is not equal to 0.
For example, if you divide 6/2 =3, so 3
is your quotient and 0 is
remainder.Hence 2*3= 6.So if your
quotient itself is 0, then in this case
numerator must be 0.So , p(x)
should be 0.Hence degrees of g(x) can
be anything.

Answer 2

Answer:

Euclid's algorithm for division