Question

If on division of a polynomial p (x) by a polynomial g (x) , the quotient is zero, what is the relation between the degrees of p (x) and g (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:

We are given with p(x)=g(x)*q(x)+r(x)

Where q(x)=0

So remainder is also 0

So if q(x) is zero so if we divide p(x)/ g(x) then p(x) must be equal to zero and the degree p(x)<degree g(x)