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Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus) Notes | Study Mathematics (Maths) Class 9 - Class 9

Document Description: Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus) for Class 9 2022 is part of Mathematics (Maths) Class 9 preparation. The notes and questions for Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus) have been prepared according to the Class 9 exam syllabus. Information about Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus) covers topics like and Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus) Example, for Class 9 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus).

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Q.1. Find the remainder when x3+3x2+3x+1 is divided by
(i) x+1
Solution:
x+1= 0
⇒ x = −1
∴ 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
∴ 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
∴ Remainder:
p(0) = (0)3+3(0)2+3(0)+1
= 1

(iv) x+π
Solution:
x+π = 0
⇒ x = −π
∴ 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
∴ Remainder:
(-5/2)3+3(-5/2)2+3(-5/2)+1 = (-125/8)+(75/4)-(15/2)+1
= -27/8


Q.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
Remainder:

p(a) = (a)3−a(a2)+6(a)−a = a3−a3+6a−a = 5a


Q.3. Check whether 7+3x is a factor of 3x3+7x.
Solution:

7+3x = 0
⇒ 3x = −7
⇒ x = -7/3
∴ 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


Check out the NCERT Solutions of all the exercises of Polynomials: 

Exercise 2.1. NCERT Solutions: Polynomials

Exercise 2.2 NCERT Solutions: Polynomials

Exercise 2.4 NCERT Solutions: Polynomials

The document Exercise 2.3 NCERT Solutions: Polynomials (Old Syllabus) Notes | Study Mathematics (Maths) Class 9 - Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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