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Class 9 Ganita ManjariClass 9 Maths Solutions | 2026–27
Chapter 2: Introduction to Linear PolynomialsPage 19All 5 Questions on This Page

Class 9 Maths Chapter 2 Exercise Set 2.1 Solutions

Step-by-step solutions for Class 9 Mathematics Ganita Manjari Chapter 2 Exercise Set 2.1 (Page 19). Covers finding degrees of polynomials, writing polynomials of given degrees, identifying coefficients, finding coefficients of missing terms, and determining constant terms.

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Key Concepts for Exercise Set 2.1

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1

Degree of a Polynomial

The degree of a polynomial in one variable is the highest power (exponent) of the variable that has a non-zero coefficient.

Highest exponent of the variable with non-zero coefficient
2

Degree of a Non-Zero Constant Polynomial

Any non-zero real constant c can be written as c · x⁰ (since x⁰ = 1 for all x ≠ 0). Hence, every non-zero constant polynomial has degree 0. The degree of the zero polynomial 0 is not defined.

c = c · x⁰ ⇒ Degree = 0 (for c ≠ 0)
3

Coefficient of a Term

The coefficient of a term is the constant factor or numerical multiplier of its variable part. Always include the preceding positive or negative sign (+ or −) as part of the coefficient.

In a · xⁿ, coefficient of xⁿ is a
4

Constructing Polynomials of a Given Degree

A polynomial of degree n can have any number of terms and arbitrary non-zero real coefficients, provided the greatest exponent of the variable is n. Therefore, there are infinitely many valid answers for any given degree.

Degree 1: ax + b | Degree 2: ax² + bx + c | Degree 3: ax³ + bx² + cx + d (a ≠ 0)
5

Coefficient of a Missing Term

If a variable power does not appear in a polynomial, its coefficient is 0. The expression can be rewritten by inserting the missing power multiplied by 0.

4z³ + 5z² − 11 = 4z³ + 5z² + 0z − 11 ⇒ Coefficient of z = 0
6

Constant Term of a Polynomial

The constant term is the term that does not contain the variable. Always preserve the preceding negative sign if the constant term is negative.

In 9x³ + 5x² − 8x − 10, constant term = −10
Question 1
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Find the degrees of the following polynomials: (i) 2x² − 5x + 3 (ii) y³ + 2y − 1 (iii) −9 (iv) 4z − 3

Solution

The degree of a polynomial is the highest power of the variable having a non-zero coefficient.

(i) 2x² − 5x + 3

The highest power of x is 2.

Therefore:
Degree = 2
(ii) y³ + 2y − 1

The highest power of y is 3.

Therefore:
Degree = 3
(iii) −9

−9 is a non-zero constant polynomial.

It can be written as:
−9 = −9x⁰

The highest power is 0.

Therefore:
Degree = 0
(iv) 4z − 3

The highest power of z is 1.

Therefore:
Degree = 1
Answer:(i) 2 | (ii) 3 | (iii) 0 | (iv) 1
Question 2
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Write polynomials of degrees 1, 2 and 3.

Solution

There are many possible answers. The only condition is that the highest power of the variable must be:

•1 for the first polynomial;
•2 for the second;
•3 for the third.

One possible set is:

Degree 1:
x + 2
Degree 2:
x² + 3x + 1
Degree 3:
x³ − 2x + 4
Therefore, one possible answer is:

x + 2, x² + 3x + 1, x³ − 2x + 4

Note
These answers are not unique. Any polynomials where the highest power of the variable is 1, 2, and 3 respectively are completely correct (for example: 3x, y² − 5, 4z³ + z).
Answer:Degree 1: x + 2 | Degree 2: x² + 3x + 1 | Degree 3: x³ − 2x + 4 (Answers are not unique; other valid examples are acceptable)
Question 3
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What are the coefficients of x² and x³ in the polynomial x⁴ − 3x³ + 6x² − 2x + 7?

Solution

The coefficient of a term is the number multiplying its variable part.

The x²-term is:
6x²
Therefore, the coefficient of x² is:
6
The x³-term is:
−3x³
Therefore, the coefficient of x³ is:
−3
Hence:
Coefficient of x² = 6
Coefficient of x³ = −3
Answer:Coefficient of x² = 6 and Coefficient of x³ = −3
Question 4
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What is the coefficient of z in the polynomial 4z³ + 5z² − 11?

Solution

The coefficient of a variable is the number multiplying that variable.

Here, the polynomial:

4z³ + 5z² − 11

has no term containing z.

We can write it as:
4z³ + 5z² + 0z − 11
Therefore, the coefficient of z is:
0
Answer:0
Question 5
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What is the constant term of the polynomial 9x³ + 5x² − 8x − 10?

Solution

The constant term is the term that does not contain the variable.

In the given polynomial:
9x³ + 5x² − 8x − 10
the term without x is:
−10
Therefore, the constant term is:
−10
Answer:−10

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