Polynomials - Class IX CBSE Mathematics | NCERT Solutions for Math Textbook Exercise 2.1

POLYNOMIALS

   Class IX NCERT (CBSE) Mathematics

   NCERT Textbook Exercise 2.1 Solved

(page 32)

Q1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

Answer:

(i) It is a polynomial in one variable x.

(ii) This expression is a polynomial in one variable y.

(iii) Since exponent of variable t in term

which is not a whole number, so this expression is not a polynomial.

(iv) Since the exponent of variable y in term

Hence, this expression is not a polynomial.

(v) No it is not a polynomial in one variable. This expression is a polynomial in 3 variables x, y, and t. 

Q2: Write the coefficients of x² in each of the following:

(i) 2 + x² + x (ii) 2 – x² + x³

Answer:

(i) The coefficient of x² is 1.

(ii) In this expression, the coefficient of x² is −1.

(iii) Here the coefficient of x² is π/2.

(iv) In the above expression, the coefficient of x² is 0.

Q3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer:  

By definition, the 'Degree of a Polynomial' is the highest power of the variable in the polynomial. 
A binomial has two terms in it. An example of binomial of degree 35 is x³⁵ + x³⁴.

A Monomial has only one term in it. An example of monomial of degree 100 is x¹⁰⁰.

Q4: Write the degree of each of the following polynomials:

Answer:

(i) It is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3.

(ii) The given polynomial has variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.

(iii) This expression is a polynomial of variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.

(iv) Since it is a constant polynomial and the degree of a constant polynomial is always 0.

Q5: Classify the following as linear, quadratic and cubic polynomial:

(i) x² + x (ii) x – x³ (iii) y + y² + 4 (iv) 1 + x (v) 3t

(vi) r² (vii) 7x³

Answer: Linear, quadratic, and cubic polynomials have degrees as 1, 2, and 3 respectively.

(i) This is a quadratic polynomial as its degree is 2.

(ii) This is a cubic polynomial as its degree is 3.

(iii) This is a quadratic polynomial and its degree is 2.

(iv) 1 + x is a linear polynomial. Its degree is 1.

(v) 3t is a linear polynomial. Its degree is 1.

(vi) r² is a quadratic polynomial as its degree is 2.

(vii) 7x³ is a cubic polynomial and its degree is 3.