Polynomial_Soln_2.3

 

NCERT Solutions for Class 9 Maths Exercise 2.3

 

Question 1. Find the remainder whenis divided by

(i)

(ii)

(iii) x

(iv)

(v)

Solution:

(i)

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomialin the polynomial, to get

=-1+3-3+1

=0

Therefore, we conclude that on dividing the polynomialby, we will get the remainder as 0.

(ii)

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomialin the polynomial, to get

Therefore, we conclude that on dividing the polynomialby, we will get the remainder as.

(iii)

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomialin the polynomial, to get

=0+0+0+1

=1

Therefore, we conclude that on dividing the polynomialby x, we will get the remainder as 1.

(iv)

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomialin the polynomial, to get

Therefore, we conclude that on dividing the polynomialby, we will get the remainder as.

(v)

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomial in the polynomial, to get

Therefore, we conclude that on dividing the polynomialby, we will get the remainder as.

Question 2. Find the remainder whenis divided by.

Solution:

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomialin the polynomial, to get

= 5a

Therefore, we conclude that on dividing the polynomialby, we will get the remainder as.

Question 3. Check whether is a factor of.

Solution:

We know that if the polynomialis a factor of, then on dividing the polynomialby, we must get the remainder as 0.

We need to find the zero of the polynomial.

While applying the remainder theorem, we need to put the zero of the polynomialinthe polynomial, to get

We conclude that on dividing the polynomialby, we will get the remainder as, which is not 0.

Therefore, we conclude thatis not a factor of.