A day full of math games & activities. Find one near you.

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)

Solution:

Given, a polynomial p(x) is divided by a polynomial g(x).

The quotient q(x) is zero.

We have to find the relation between the degrees of p(x) and g(x).

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

p(x) = g(x) (0) + (0)

p(x) = 0

Therefore, the relation is that the degree of p(x) is less than the degree of g(x).

✦ Try This: If on division of a polynomial r(x) by a polynomial s(x), the quotient is zero, what is the relation between the degrees of r(x) and s(x)

Given, a polynomial r(x) is divided by a polynomial s(x).

The quotient q(x) is zero.

We have to find the relation between the degrees of r(x) and s(x).

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

r(x) = s(x) (0) + (0)

r(x) = 0

Therefore, the relation is that the degree of r(x) is less than the degree of s(x)

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 1 (iii)

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)

Summary:

If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, the relation between the degrees of p(x) and g(x) is that the degree of p(x) is less than the degree of g(x)

☛ Related Questions: