Exercise 2.1 Practice
00:00
Overview
This page provides comprehensive Ch 2: Polynomials - Exercise 2.1 Practice. Free NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2-1. Step-by-step explained answers for CBSE Board exams. Download PDF and practice now.
Introduction to Polynomials
Q1: Polynomial Degrees
Find the degrees of the following polynomials:
(i) $2x^2 - 5x + 3$
(ii) $y^3 + 2y - 1$
(iii) $-9$
(iv) $4z - 3$
(i) $2x^2 - 5x + 3$
(ii) $y^3 + 2y - 1$
(iii) $-9$
(iv) $4z - 3$
The degree of a polynomial is the highest exponent of the variable in the polynomial.
(i) $2x^2 - 5x + 3$: The variable is $x$. The highest exponent of $x$ is $2$.
Degree = **$2$**.
Degree = **$2$**.
(ii) $y^3 + 2y - 1$: The variable is $y$. The highest exponent of $y$ is $3$.
Degree = **$3$**.
Degree = **$3$**.
(iii) $-9$: This is a non-zero constant polynomial. It can be written as $-9y^0$.
Degree = **$0$**.
Degree = **$0$**.
(iv) $4z - 3$: The variable is $z$. The highest exponent of $z$ is $1$ ($4z^1$).
Degree = **$1$**.
Degree = **$1$**.
(i) 2, (ii) 3, (iii) 0, (iv) 1
Q2: Write Polynomials
Write polynomials of degrees 1, 2 and 3.
A polynomial of degree 1 is a linear polynomial.
Example: $3x + 5$
Example: $3x + 5$
A polynomial of degree 2 is a quadratic polynomial.
Example: $x^2 - 4x + 4$
Example: $x^2 - 4x + 4$
A polynomial of degree 3 is a cubic polynomial.
Example: $2x^3 - x^2 + 5$
Example: $2x^3 - x^2 + 5$
e.g., Degree 1: $3x + 5$; Degree 2: $x^2 - 4x + 4$; Degree 3: $2x^3 - x^2 + 5$
Q3: Find Coefficients
What are the coefficients of $x^2$ and $x^3$ in the polynomial $x^4 - 3x^3 + 6x^2 - 2x + 7$?
Identify the terms of the polynomial:
The term containing $x^3$ is $-3x^3$.
The term containing $x^2$ is $6x^2$.
The term containing $x^3$ is $-3x^3$.
The term containing $x^2$ is $6x^2$.
The coefficient of a term is the numerical factor multiplying the variable.
- For $-3x^3$, the coefficient is $-3$.
- For $6x^2$, the coefficient is $6$.
Coefficient of $x^2$ = 6, Coefficient of $x^3$ = -3
Q4: Coefficient of z
What is the coefficient of $z$ in the polynomial $4z^3 + 5z^2 - 11$?
Examine the given polynomial: $4z^3 + 5z^2 - 11$.
The polynomial has no term in $z$ (or $z^1$). It can be written as:
$$4z^3 + 5z^2 + 0z - 11$$
The coefficient of $z$ is 0.
Q5: Constant Term
What is the constant term of the polynomial $9x^3 + 5x^2 - 8x - 10$?
The constant term of a polynomial is the term that does not depend on the variable $x$.
In $9x^3 + 5x^2 - 8x - 10$, the independent term is $-10$.
Constant term = -10