NCERT Solutions for Class 10 Maths Exercise 2.2 Chapter 2 Polynomials – FREE PDF Download
NCERT Class 10 Maths Ch 2 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths Chapter 2 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Polynomials solutions will help you understand the chapter thoroughly.
NCERT Solutions for Class 10 Maths Chapter 2 – 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
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.
3. Obtain all other zeroes of 
if two of its zeroes are 
and 
.
Ans. Two zeroes of 
are and which means that 
= 3x2−53×2−5 is a factor of .
Applying Division Algorithm to find more factors we get:
We have 
⇒ 
= (3x2−5)(x2+2x+1)(3×2−5)(x2+2x+1)
= (3x2−5)(x+1)(x+1)(3×2−5)(x+1)(x+1)
Therefore, other two zeroes of are −1 and −1.
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) = 
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