**Chapter 2 Polynomials**

**Ex 2.1**

**Ex 2.1 Class 9
Maths Question 1.**

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

(i) 4x^{2} – 3x + 7

(ii) y^{2} + √2

(iii) 3 √t + t√2

(iv) y+

(v) x^{10}+ y^{3}+t^{50}

Solution:

(i) We have 4x^{2} – 3x + 7 = 4x^{2} – 3x + 7x^{0}

It is a polynomial in one variable i.e., x

because each exponent of x is a whole number.

**(ii) We have y ^{2} + √2 = y^{2} + √2y^{0}**

It is a polynomial in one variable i.e., y

because each exponent of y is a whole number.

**(iii) We have 3 √t + t√2 = 3 √t ^{1/2} + √2.t
It is not a polynomial, because one of the exponents of t is
**

**(iv) We have y +
**

**(v) We have x ^{10}+ y^{3 }+ t^{50}**

Here, exponent of every variable is a whole number, but x^{10} + y^{3} + t^{50} is a polynomial in x, y and t, i.e., in three variables.

So, it is not a polynomial in one variable.

**Ex 2.1 Class 9
Maths Question 2.**

Write the coefficients of x^{2} in each of the following

(i) 2 + x^{2} + x

(ii) 2 – x^{2} + x^{3}

(iii) **x ^{2} + x
(iv) √2 x – 1**

Solution:

(i) The given polynomial is 2 + x

The coefficient of x

(ii) The given polynomial is 2 – x

The coefficient of x

(iii) The given polynomial is
+ x.

The coefficient of x
.

(iv) The given polynomial is √2 x – 1.

The coefficient of x

Solution:

(i) The given polynomial is 2 + x

^{2}+ x.The coefficient of x

^{2}is 1.(ii) The given polynomial is 2 – x

^{2}+ x^{3}.The coefficient of x

^{2}is -1.(iii) The given polynomial is

The coefficient of x

^{2}is(iv) The given polynomial is √2 x – 1.

The coefficient of x

^{2}is 0.**Ex 2.1 Class 9
Maths Question 3.**

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

Solution:

(i) Abmomial of degree 35 can be 3x^{35} -4.

(ii) A monomial of degree 100 can be √2y^{100}.

**Ex 2.1 Class 9
Maths Question 4.**

Write the degree of each of the following polynomials.

(i) 5x^{3}+4x^{2} + 7x

(ii) 4 – y^{2 }

(iii) 5t – √7

(iv) 3

Solution:

(i) The given polynomial is 5x^{3} + 4x^{2} + 7x.

The highest power of the variable x is 3.

So, the degree of the polynomial is 3.

(ii) The given polynomial is 4- y^{2}. The highest

power of the variable y is 2.

So, the degree of the polynomial is 2.

(iii) The given polynomial is 5t – √7. The highest power of variable t is 1.
So, the degree of the polynomial is 1.

(iv) Since, 3 = 3x° [**∵**** x°=1]
So, the degree of the polynomial is 0.**

**Ex 2.1 Class 9
Maths Question 5****.
Classify the following as linear, quadratic and cubic polynomials.
(i) x**

^{2}+ x (ii) x – x

^{3}(iii) y + y

^{2}+4 (iv) 1 + x (v) 3t (vi) r

^{2}(vii) 7x

^{3}

^{ }**Solution:**

(i) The degree of x

(ii) The degree of x – x

(iii) The degree of y + y

(iv) The degree of 1 + x is 1. So, it is a linear polynomial.

(v) The degree of 3t is 1. So, it is a linear polynomial.

(vi) The degree of r

(vii) The degree of 7x

(i) The degree of x

^{2}+ x is 2. So, it is a quadratic polynomial.(ii) The degree of x – x

^{3}is 3. So, it is a cubic polynomial.(iii) The degree of y + y

^{2}+ 4 is 2. So, it is a quadratic polynomial.(iv) The degree of 1 + x is 1. So, it is a linear polynomial.

(v) The degree of 3t is 1. So, it is a linear polynomial.

(vi) The degree of r

^{2}is 2. So, it is a quadratic polynomial.(vii) The degree of 7x

^{3}is 3. So, it is a cubic polynomial.
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