In this post, we provide a clear, step-by-step solution for Class 9 Maths Chapter 2 (Polynomials), Exercise 2.1. We have broken down every question to ensure that both English and Hindi medium students can follow the logic easily. This is a crucial chapter for building your foundation in Algebra.
Exercise 2.1 Solutions
Q1: Which of the following expressions are polynomials in one variable and which are not? State reasons.
(i) 4x² - 3x + 7
Solution: Yes, it is a polynomial in one variable (x) because the exponents are whole numbers.
(ii) y² + √2
Solution: Yes, it is a polynomial in one variable (y).
(iii) 3√t + t√2
Solution: No, because the exponent of 't' in 3√t (which is t1/2) is not a whole number.
Q2: Write the coefficients of x² in each of the following:
(i) 2 + x² + x
Solution: The coefficient of x² is 1.
(ii) 2 - x² + x³
Solution: The coefficient of x² is -1.
Q3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution: Binomial of degree 35: x³⁵ + 1. Monomial of degree 100: x¹⁰⁰.
Aptitude Corner: Remember, in competitive exams like NTSE or IMO, always verify that the powers are non-negative integers before calling an expression a polynomial!
Academic Discussion & Doubts