2. Polynomials Mathematics Exercise - 2.1 class 9 Maths in English - CBSE Study
NCERT Solutions for Class 9 Mathematics are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important 2. Polynomials with detailed explanations and step-by-step answers for better exam preparation. Each Exercise 2.1 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 9 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics.
Class 9 English Medium Mathematics All Chapters:
2. Polynomials
1. Exercise 2.1
Exercise 2.1
Q1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii)3√t + t√2
(iv) y +2/y
(v) x10 + y3 + t50
Solution:
(i) 4x2 – 3x + 7
It is polynomial in one variable. Because the power of variable is natural number.
(ii) y2 + √2
It is polynomial in one variable. Because the power of variable is natural number.
(iii)3√t + t√2
It is not a polynomial in one variable. Because the power of variable is not a natural number, it is a fractional number.
(iv) y +2/y
It is not a polynomial in one variable.
(v) x10 + y3 + t50
It is not a polynomial in one variable. while It is a polynomial in three variable.
Q2. Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x
(ii) 2 – x2 + x3 (
iii) π/2 x2 + x
(iv) √2x −1
Solution:
(i) 2 + x2 + x
Coefficient of x2 = 1
(ii) 2 – x2 + x3
Coefficient of x2 = –1
(iii) π/2 x2 + x
Coefficient of x2 = π/2
(iv) √2x −1
Coefficients of x2 = 0 [Because There is no x2 So coefficient will be 0]
Q3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
A binomial of degree 35
⇒ 2x35 + 5y
Note: Binomial means the expression of two terms. Like x + 5, 3a - 2b, 3t + 7 etc.
A monomial of degree 100
⇒ 3y100
Note: Monomial means the expression of single term, like 3x, 5t, y, 3xy etc.
Q4. Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x
(ii) 4 – y2
(iii) 5t – √7
(iv) 3
Solution:
(i) 5x3 + 4x2 + 7x
Ans: The degree of polynomial = 3 [Highest power]
(ii) 4 – y2
Ans: The degree of polynomial = 2
(iii) 5t – √7
Ans: The degree of polynomial = 1
(iv) 3
Ans: The degree of polynomial = 0
[Note: There is no variable therefore degree = 0]
Q5. Classify the following as linear, quadratic and cubic polynomials:
(i) x2 + x
(ii) x – x3
(iii) y + y2 + 4
(iv) 1 + x
(v) 3t
(vi) r2
(vii) 7x2
Solution:
(i) x2 + x
Ans: Quadratic polynomial
(ii) x – x3
Ans: Cubic polynomial
(iii) y + y2 + 4
Ans: Quadratic polynomial
(iv) 1 + x
Ans : Linear polynomial
(v) 3t
Ans : Linear polynomial
(vi) r2
Ans: Quadratic polynomial
(vii) 7x2
Ans: Cubic polynomial
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