**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 termHence, 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 x

^{2 }in each of the following:(i) 2 + x

^{2 }+ x (ii) 2 – x^{2}+ x^{3}Answer:

(i) The coefficient of x

^{2}is 1.(ii) In this expression, the coefficient of x

^{2}is −1.(iii) Here the coefficient of x

^{2}is π/2.(iv) In the above expression, the coefficient of x

^{2}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 x

A binomial has two terms in it. An example of binomial of degree 35 is x

^{35}+ x^{34}.A Monomial has only one term in it. An example of monomial of degree 100 is

*x*^{100}.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) x

^{2}+ x (ii) x – x^{3}(iii) y + y^{2}+ 4 (iv) 1 + x (v) 3*t*(vi)

*r*(vii) 7x^{2}^{3}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)

*r*is a quadratic polynomial as its degree is 2.^{2}(vii) 7x

^{3}is a cubic polynomial and its degree is 3.
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