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NCERT Solutions for Class 9 Maths Chapter 2 - Exercise 2.3 Polynomials (Old Syllabus)

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 NCERT Solutions for Class 9 Maths Chapter 2 - Exercise 2.3 Polynomials (Old Syllabus) is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on NCERT Solutions for Class 9 Maths Chapter 2 - Exercise 2.3 Polynomials (Old Syllabus)

1. What are polynomials in mathematics?
Ans. Polynomials are algebraic expressions consisting of variables, coefficients, and exponents that can be added, subtracted, multiplied, and divided.
2. How do you classify polynomials based on the number of terms?
Ans. Polynomials can be classified as monomials (one term), binomials (two terms), trinomials (three terms), or polynomials with more than three terms.
3. What is the degree of a polynomial?
Ans. The degree of a polynomial is the highest power of the variable in the expression. It helps determine the behavior of the polynomial function.
4. How can polynomials be used in real-life applications?
Ans. Polynomials are used in various fields like engineering, physics, and economics to model and solve real-world problems, such as calculating areas, volumes, or predicting trends.
5. Can polynomials be graphed on a coordinate plane?
Ans. Yes, polynomials can be graphed on a coordinate plane to visualize their behavior, roots, and turning points, which helps in understanding their properties and relationships.
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