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 can use it for reference while solving the exercise problems. The third exercise in NCERT Class 9 Maths Solutions Chapter 2 Polynomials – Exercise 2.3 discusses an important theorem – The Remainder Theorem.
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NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials Exercise 2.3
Access Answers to Maths NCERT Class 9 Chapter 2 – Polynomials Exercise 2.3
1. Find the remainder when x3+3x2+3x+1 is divided by
(i) x+1
Solution:
x+1= 0
⇒x = −1
∴ The remainder:
p(−1) = (−1)3+3(−1)2+3(−1)+1
= −1+3−3+1
= 0
(ii) x−1/2
Solution:
x-1/2 = 0
⇒ x = 1/2
∴ The 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
∴ The remainder:
p(0) = (0)3+3(0)2+3(0)+1
= 1
(iv) x+Ï€
Solution:
x+Ï€ = 0
⇒ x = −π
∴ The remainder:
p(0) = (−π)3 +3(−π)2+3(−π)+1
= −π3+3π2−3π+1
(v) 5+2x
Solution:
5+2x=0
⇒ 2x = −5
⇒ x = -5/2
∴ The 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 when x3−ax2+6x−a is divided by x-a.
Solution:
Let p(x) = x3−ax2+6x−a
x−a = 0
∴ x = a
The remainder:
p(a) = (a)3−a(a2)+6(a)−a
= a3−a3+6a−a = 5a
3. Check whether 7+3x is a factor of 3x3+7x.
Solution:
7+3x = 0
⇒ 3x = −7
⇒ x = -7/3
∴ The remainder:
3(-7/3)3+7(-7/3) = -(343/9)+(-49/3)
= (-343-(49)3)/9
= (-343-147)/9
= -490/9 ≠0
∴ 7+3x is not a factor of 3x3+7x
Access Other Exercise Solutions of Class 9 Maths Chapter 2 – Polynomials
From the links below, students can get the NCERT Solutions for Class 9 Maths Chapter 2.
Exercise 2.1 Solutions 5 Questions
Exercise 2.2 Solutions 4 Questions
Exercise 2.4 Solutions 5 Questions
Exercise 2.5 Solutions 16 Questions
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 +
so what is the answer please send the answer in the email id
thank you
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
⇒ x = −π
p(0) = (−π)^3 +3(−π)^2+3(−π)+1
Here, in accordance with your doubt,
We understand you have a confusion regarding: +3(−π)^2
In this case, we have to square (-Ï€), Hence,
(−π)^2 = π^2
Therefore,
+3(−π)^2 = +3π^2
Now, we get the final answer as:
= −π^3+3π^2−3π+1