Gujarat Board GSEB Solutions Class 9 Maths Chapter 2 Polynomials Ex 2.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 9 Maths Chapter 2 Polynomials Ex 2.1

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} + \(\sqrt{2}\)

(iii) 3\(\sqrt{t}\) + t\(\sqrt{2}\)

(iv) y + \(\frac { 1 }{ 2 }\)

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

Solution:

(i) 4x^{2} – 3x + 7

This is a polynomial in one variable x whose powers are non-negative integers. So this polynomial is in one variable.

(ii) y^{2} + y\(\sqrt{2}\)

This polynomial is in one variable y whose exponents are in whole numbers. So this polynomial is in one variable.

(iii) 3\(\sqrt{t}\) + t\(\sqrt{2}\)

This is not a polynomial because exponent of t is \(\frac { 1 }{ 2 }\) which is not a whole number.

(iv) y + \(\frac { 2 }{ y }\) This is not a polynomial because exponent \(\frac { 2 }{ y }\) of i.e., 2y^{-1} is negative which is not a whole number. So this is not a polynomial in one variable.

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

This polynomial is in three variables x, y and t. Their exponents are in whole numbers. So this is a polynomial in three variables.

Question 2.

Write the coefficients of x2 in each of the following:

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

(ii) 2 – x^{2} + x^{3}

(iii) \(\frac { Ï€ }{ y }\) x^{2} + x

(iv) \(\sqrt{t}\) – 1

Solution:

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

Coefficient of x^{2} = 1

(ii) 2 – x^{2} + x^{3}

Coefficient of x^{3} = – 1

(iii) \(\frac { Ï€ }{ 2 }\) x^{2} + x

Coefficient of x^{2} = 0

(iv) \(\sqrt{2x}\) – 1

Coefficient of x^{2} = 0

Question 3.

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

Solution:

5x^{35} + 9 and 7x^{100}.

Question 4.

Write the degree of each of the following polynomials:

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

(ii) 4 – y^{2}

(iii) 5t – \(\sqrt{7}\)

(iv) 3

Solution:

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

The term 5x^{3} is highest power in x whose power is 3. Therefore degree of polynomial is 3.

(ii) 4 – y^{2}

-y^{2} is highest power iny which has power 2.

S0 degree of polynomial is 2.

(iii) 5t – \(\sqrt{7}\)

5t has highest power in t which has power 1. So degree of polynomial is 1.

(iv) 3 has no variable i.e., exponent of variable is 0. Therefore degree of constant polynomial is 0.

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) x^{2} + x Quadratic (Highest degree 2)

(ii) x – x^{3} Cubic (Highest degree 3)

(iii) y + y^{2} + 4 Quadratic (Highest degree 2)

(iv) 1 + x Linear (Highest degree 1)

(v) 3t Linear (Highest degree 1)

(vi) r^{2} Quadratic (Highest degree 2)

(vii) 7x^{3} Cubic (Highest degree 3)