# NCERT Solutions for class 9 Maths Chapter 2- Polynomials Exercise 2.3

NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.3 are provided here. These NCERT Maths solutions are prepared by our subject experts which makes it easy for students to learn. The students use it for reference while solving the exercise problems. The third exercise in Polynomials- Exercise 2.3 discusses the important theorem â€“ The Remainder Theorem. Our experts provide detailed and stepwise explanations of each answer to the questions given in the exercises in the NCERT textbook for Class 9. The NCERT solutions are always prepared by following NCERT guidelines so that it covers the whole syllabus accordingly. These are very helpful in scoring well in first and second term examinations.

## Download PDF of NCERT Solutions for Class 9 Maths Chapter 2- Polynomials Exercise 2.3

### Access Answers of Maths NCERT Class 9 Chapter 2 â€“ Polynomials Exercise 2.3

1. Find the remainder whenÂ x3+3x2+3x+1Â is divided by

(i) x+1

Solution:

x+1= 0

â‡’x = âˆ’1

âˆ´Remainder:

p(âˆ’1) = (âˆ’1)3+3(âˆ’1)2+3(âˆ’1)+1

= âˆ’1+3âˆ’3+1

= 0

(ii) xâˆ’1/2

Solution:

x-1/2 = 0

â‡’ x = 1/2

âˆ´Remainder:

p(1/2) = (1/2)3+3(1/2)2+3(1/2)+1

= (1/8)+(3/4)+(3/2)+1

= 27/8

(iii) x

Solution:

x = 0

âˆ´Remainder:

p(0) = (0)3+3(0)2+3(0)+1

= 1

(iv) x+Ï€

Solution:

x+Ï€ = 0

â‡’ x = âˆ’Ï€

âˆ´Remainder:

p(0) = (âˆ’Ï€)3 +3(âˆ’Ï€)2+3(âˆ’Ï€)+1

= âˆ’Ï€3+3Ï€2âˆ’3Ï€+1

(v) 5+2x

Solution:

5+2x=0

â‡’ 2x = âˆ’5

â‡’ x = -5/2

âˆ´Remainder:

(-5/2)3+3(-5/2)2+3(-5/2)+1 = (-125/8)+(75/4)-(15/2)+1

= -27/8

2. Find the remainder whenÂ x3âˆ’ax2+6xâˆ’aÂ is divided by x-a.

Solution:

LetÂ p(x) = x3âˆ’ax2+6xâˆ’a

xâˆ’a = 0

âˆ´x = a

Remainder:

p(a) = (a)3âˆ’a(a2)+6(a)âˆ’a

= a3âˆ’a3+6aâˆ’a = 5a

3. Check whether 7+3x is a factor ofÂ 3x3+7x.

Solution:

7+3x = 0

â‡’ 3x = âˆ’7

â‡’ x = -7/3

âˆ´Remainder:

3(-7/3)3+7(-7/3) = -(343/9)+(-49/3)

= (-343-(49)3)/9

= (-343-147)/9

= -490/9 â‰  0

âˆ´7+3x is not a factor ofÂ 3x3+7x

### Access other exercise solutions of Class 9 Maths Chapter 2- Polynomials

Exercise 2.1 Solutions 5 Questions
Exercise 2.2 Solutions 4 Questions
Exercise 2.4 Solutions 5 Questions
Exercise 2.5 Solutions 16 Questions

1. sudeep.n

sir or mam i have a doubt that in Ex. 2.3
1. 4 in the last second step after -pai whole cube there is +3(-pai)square but + x – is – but you wrote +
thank you

1. Hy Sudeep.n
In that particular question:
1.Find the remainder when x^3+3x^2+3x+1 is divided by
(iv) x+Ï€
Solution:
x+Ï€ = 0
â‡’ x = âˆ’Ï€
p(0) = (âˆ’Ï€)^3 +3(âˆ’Ï€)^2+3(âˆ’Ï€)+1
Here, in accordance with your doubt,
We understand you have a confusion regarding: +3(âˆ’Ï€)^2
In this case, we have to square (-Ï€), Hence,
(âˆ’Ï€)^2 = Ï€^2
Therefore,
+3(âˆ’Ï€)^2 = +3Ï€^2
Now, we get the final answer as:
= âˆ’Ï€^3+3Ï€^2âˆ’3Ï€+1