NCERT Class 9 Maths Chapter 2 Polynomials Exercise 2.1

Chapter 2 Polynomials Exercise 2.1

Question 1: 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
Answer:
i) and ii) are polynomials in one variable.
v) is a polynomial in three variable.
iii) and iv) are not polynomials as in each of these exponent of the variable is not a whole number.

Question 2: Write the coefficients of x² in each of the following:
i)  2 + x² + x
ii) 2 - x² + x³
iii) π/2 x² + x
iv) √2 x - 1
Answer:
i) 1
ii) -1
iii) π/2
iv) 0

Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Answer:
Binomial of degree 35: x³⁵ - 5
Monomial of degree 100: y¹⁰⁰

Question 4: Write the degree of each of the following polynomials:
i)  5x³ + 4x² + 7x
ii) 4 - y²
iii) 5t - √7
iv) 3
Answer:
i) 3
ii) 2
iii) 1
iv) 0

Question 5: 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) 7x³
Answer:
i) Quadratic
ii) Cubic
iii) Quadratic
iv) Linear
v) Linear
vi) Quadratic
vii) Cubic