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

We know that,

p(x) = g(x) × q(x) + r(x)

According to the question,

q(x) = 0

When q(x) = 0, then r(x) is also = 0

So, now when we divide p(x) by g(x),

Then p(x) should be equal to zero

Hence, the relation between the degrees of p(x) and g(x) is the degree p(x) < degree g(x).