NCERT Solutions for Class 9th Maths Chapter 2 Exercise Set 2.1 — Introduction

Book page 18–19 Updated on2026-09-08

Q1.

Find the degrees of the following polynomials: (i) 2x² – 5x + 3 (ii) y³ + 2y – 1 (iii) – 9 (iv) 4z – 3

Answer

The degree is the highest power of the variable that actually appears.

Polynomial	Powers present	Degree	Name
(i) 2x² − 5x + 3	2, 1, 0	2	quadratic
(ii) y³ + 2y − 1	3, 1, 0	3	cubic
(iii) −9	0 only	0	constant
(iv) 4z − 3	1, 0	1	linear

Why (iii) has degree 0 and not “no degree”: −9 can be written as −9x⁰, since x⁰ = 1 for every x ≠ 0. The variable is there, carrying the power 0, so the highest power present is 0. Notice too that in (ii) the y² term is missing; a missing term simply has coefficient 0 and does not affect the degree, which is decided by the largest power with a non-zero coefficient.

Tip: Degree is read off the exponents, never off the coefficients. 2x² − 5x + 3 has degree 2 even though 5 and 3 are bigger numbers than 2.

Q2.

Write polynomials of degrees 1, 2 and 3.

Answer

Any expression in one variable whose highest power is the required number will do. For example:

Degree 1 (linear): 3x + 7
Degree 2 (quadratic): x² − 4x + 1
Degree 3 (cubic): 2x³ + x − 5

What has to be checked: only two things. First, exactly one variable must appear — 3x + 7y is not a univariate polynomial. Second, the leading coefficient must not be zero: in 2x³ + x − 5 the number multiplying x³ is 2, which is non-zero, so the degree really is 3. Lower terms may be missing freely — x³ on its own is a perfectly good cubic.

Try This: write three more of each, using different letters (t, m, z) and at least one negative coefficient, then swap with a friend and check the degrees.

Q3.

What are the coefficients of x² and x³ in the polynomial x⁴ – 3x³ + 6x² – 2x + 7?

Answer

Read the number attached to each power, together with the sign in front of it.

x⁴ − 3x³ + 6x² − 2x + 7
Coefficient of x² = 6
Coefficient of x³ = −3

Why the sign is part of the answer: the polynomial is a sum of terms, so “− 3x³” is really “+ (−3)x³”. If you drop the minus, substituting a number gives the wrong value: at x = 1 the true value is 1 − 3 + 6 − 2 + 7 = 9, but with +3 you would get 15.

Tip: the coefficient of x⁴ here is 1 (an unwritten 1), and the constant term 7 is the coefficient of x⁰.

Q4.

What is the coefficient of z in the polynomial 4z³ + 5z² – 11?

Answer

There is no z term written, so its coefficient is

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

Why 0 and not “none”: a polynomial of degree 3 has room for all four powers z³, z², z, z⁰. A power that is not printed is present with coefficient 0 — adding 0·z changes nothing, so the two ways of writing the polynomial are the same object. Saying the coefficient is 0 keeps the list of coefficients complete: 4, 5, 0, −11.

Check it yourself: at z = 2, 4(8) + 5(4) − 11 = 32 + 20 − 11 = 41, and adding 0·2 leaves it at 41.

Q5.

What is the constant term of the polynomial 9x³ + 5x² – 8x –10?

Answer

The constant term is the one with no x in it.

9x³ + 5x² − 8x − 10
Constant term = −10

Why it is worth naming: the constant term is the value of the polynomial when the variable is 0. Substituting x = 0 kills every other term: 9(0) + 5(0) − 8(0) − 10 = −10. So the constant term is the “starting value” of the input–output machine, and later in this chapter it is exactly the b of y = ax + b — the y-intercept.

Tip: Keep the minus sign with the 10. “10” would be the constant of a different polynomial.

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