Exercise Set 2.1 Class 9 · Ganita Manjari
📘 Chapter 2 — Polynomials
📌 Complete Solutions
📐
Degree of a polynomial is the highest power of the variable in the polynomial.
A polynomial of degree 1 is called a linear polynomial,
degree 2 is a quadratic polynomial, and
degree 3 is a cubic polynomial.
1
Find the degrees of the following polynomials:
(i) 2x² − 5x + 3
(ii) y³ + 2y − 1
(iii) −9
(iv) 4z − 3
(i) 2x² − 5x + 3
(ii) y³ + 2y − 1
(iii) −9
(iv) 4z − 3
Degree of a polynomial is the highest power of the variable.
(i)
2x² − 5x + 3
Highest power of x = 2
✅
∴ Degree = 2
(ii)
y³ + 2y − 1
Highest power of y = 3
✅
∴ Degree = 3
(iii)
−9
This is a constant polynomial (no variable)
✅
∴ Degree = 0
(iv)
4z − 3
Highest power of z = 1
✅
∴ Degree = 1
2
Write polynomials of degrees 1, 2 and 3.
Degree 1 (Linear)
2x + 5
Degree 2 (Quadratic)
x² + 3x + 1
Degree 3 (Cubic)
x³ − 2x² + x + 4
3
What are the coefficients of x² and x³ in the polynomial x⁴ − 3x³ + 6x² − 2x + 7?
Given polynomial: x⁴ − 3x³ + 6x² − 2x + 7
📌
Coefficient of x³ = −3
Coefficient of x² = 6
Coefficient of x² = 6
4
What is the coefficient of z in the polynomial 4z³ + 5z² − 11?
The given polynomial is 4z³ + 5z² − 11.
There is no term containing z¹ (i.e., z).
⚠️
Hence, the coefficient of z is 0.
5
What is the constant term of the polynomial 9x³ + 5x² − 8x − 10?
Recall that polynomials of degree 1 are called linear polynomials. In this chapter, we shall study linear polynomials.
Recall that polynomials of degree 1 are called linear polynomials. In this chapter, we shall study linear polynomials.
The constant term is the term without any variable.
In the polynomial 9x³ + 5x² − 8x − 10,
✅
the constant term is −10.