knowledge-base/class_9/ch2/0124_algebra.md

---
source: ncert_exercises
topic: algebra
class_level: class_9
chapter: ch2
exercise: ex2.1
difficulty: beginner
---

Class 9 | Ch2: Polynomials | Exercise 2.1

Q1. Which of the following expressions are polynomials in one variable? State reasons.
(i) 4x² - 3x + 7  (ii) y² + √2  (iii) 3√t + t√2  (iv) y + 2/y  (v) x¹⁰ + y³ + t⁵⁰
Answer:
(i) 4x²-3x+7 → YES. All exponents of x are whole numbers (2,1,0). ✅
(ii) y²+√2 → YES. Only variable y, exponent 2 is whole number. √2 is constant. ✅
(iii) 3√t+t√2 = 3t^(1/2)+√2·t → NO. Exponent 1/2 is not a whole number. ✅
(iv) y+2/y = y+2y^(-1) → NO. Exponent -1 is not a whole number. ✅
(v) x¹⁰+y³+t⁵⁰ → NOT polynomial in ONE variable. Has three variables x,y,t. ✅

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
Answer: (i) 1. (ii) -1. (iii) π/2. (iv) 0 (no x² term). ✅

Q3. Give one example each of a binomial of degree 35 and monomial of degree 100.
Answer: Binomial of degree 35: x³⁵+1 (two terms, highest degree 35). Monomial of degree 100: x¹⁰⁰ (one term, degree 100). ✅

Q4. Write the degree of each polynomial:
(i) 5x³+4x²+7x  (ii) 4-y²  (iii) 5t-√7  (iv) 3
Answer: (i) Degree 3 (highest power of x). (ii) Degree 2. (iii) Degree 1. (iv) Degree 0 (constant). ✅

Q5. Classify as linear, quadratic or cubic:
(i) x²+x  (ii) x-x³  (iii) y+y²+4  (iv) 1+x  (v) 3t  (vi) r²  (vii) 7x³
Answer: (i) Quadratic (degree 2). (ii) Cubic (degree 3). (iii) Quadratic (degree 2). (iv) Linear (degree 1). (v) Linear (degree 1). (vi) Quadratic (degree 2). (vii) Cubic (degree 3). ✅