Polynomials Exercise 2.3
NCERT solutions for Class 10 Maths Polynomials
NCERT Solutions for Class 10 Maths Polynomials
1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.
(i)
, 
(ii)
, 
(iii)
, 
Ans. (i)
Therefore, quotient = x – 3 and Remainder = 7x – 9
(ii)
Therefore, quotient = 
and, Remainder = 8
(iii)
Therefore, quotient = 
and, Remainder = −5x + 10
NCERT Solutions for Class 10 Maths Exercise 2.3
2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
(i) 
(ii) 
(iii) 
Ans. (i)
Remainder = 0
Hence first polynomial is a factor of second polynomial.
(ii)
Remainder = 0
Hence first polynomial is a factor of second polynomial.
(iii)
Remainder ≠0
Hence first polynomial is not factor of second polynomial.
NCERT Solutions for Class 10 Maths Exercise 2.3
3. Obtain all other zeroes of 
if two of its zeroes are 
and 
.
Ans. Two zeroes of 
are and which means that 
is a factor of .
Applying Division Algorithm to find more factors we get:
We have 
⇒ 
= (
)
= ()3
= 3()
= 3()(x+1)(x+1)
Therefore, other two zeroes of are −1 and −1.
NCERT Solutions for Class 10 Maths Exercise 2.3
4. On dividing 
by a polynomial g(x), the quotient and remainder were (x-2) and (-2x+4) respectively. Find g(x).
Ans. Let
, q(x) = (x – 2) and r(x) = (–2x+4)
According to Polynomial Division Algorithm, we have
p(x) = g(x).q(x) + r(x)
⇒ 
= g(x).(x−2)−2x+4
⇒ 
−4 = g(x).(x−2)
⇒ 
= g(x).(x−2)
⇒ g(x) = 
So, Dividing 
by (x−2), we get
Therefore, we have g(x) = 
NCERT Solutions for Class 10 Maths Exercise 2.3
5. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
Ans. (i) Let 
, g(x) = 3
So, we can see in this example that deg p(x) = deg q(x) = 2
(ii) Let 
and 
We can see in this example that deg q(x) = deg r(x) = 1
(iii) Let
, g(x) = x+3
We can see in this example that deg r(x) = 0