Rajasthan Board RBSE Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 Textbook Exercise Questions and Answers.

## RBSE Class 9 Maths Solutions 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) 4x^{2} – 3x + 7

Answer:

In 4x^{2} – 3x + 7, all the exponents of x are whole numbers. So, it is a polynomial in one variable x.

(ii) y^{2} + √2

Answer:

In y^{2} + √2, the exponent of y is a whole number. So, it is a polynomial in one variable y.

(iii) 3 √t + t√2

Answer:

3 √t + t√2 = 3^{\(\frac{1}{2}\)} + t√2. Here the exponent of t in the first term is \(\frac{1}{2}\), which is not a whole number. Therefore, it is not a polynomial.

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

Answer:

y + \(\frac{2}{y}\) = y + 2y^{-1}. Here the exponent of y in the second term is – 1, which is not a whole number and so it is not a polynomial.

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

Answer:

x^{10} + y^{3} + t^{50} is not a polynomial in one variable as three variables x, y and t occur in it. However, it is a polynomial in three variables x, y and t.

Question 2.

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

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

Answer:

Coefficient of x^{2}: 1

(ii) 2 – x^{2} + x^{3}

Answer:

Coefficient of x^{2}: – 1

(iii) \(\frac{π}{2}\)x^{2} + x

Answer:

Coefficient of x^{2}: \(\frac{π}{2}\)

(iv) √2x – 1

Answer:

Coefficient of x^{2}: 0

Question 3.

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

Answer:

(i) Binomial of degree 35 may be taken as 5x^{35} + 26x.

(ii) Monomial of degree 100 may be taken as 7x^{100}.

Question 4.

Write the degree of each of the following polynomials :

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

Answer:

The highest power term is 5×3 and its exponent is 3. So, its degree is 3.

(ii) 4 – y^{2}

Answer:

The highest power term is – y^{2} and the exponent is 2. So, its degree is 2.

(iii) 5t – √7

Answer:

The highest power term is 51 and the exponent is 1. So, its degree is 1.

(iv) 3

Answer:

The only term here is 3 which can be written as 3x° and so the exponent is 0. Therefore, its degree is 0.

Question 5.

Classify the following as linear, quadratic and cubic polynomials :

(i) x^{2} + x

Answer:

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

(ii) x – x^{3}

Answer:

The degree of x – x^{3} is 3. So, it is a cubic polynomial.

(iii) y + y^{2} + 4

Answer:

The degree of y + y^{2} + 4 is 2. So, it is a quadratic polynomial.

(iv) 1 + x

Answer:

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

(v) 3t

Answer:

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

(vi) r^{2}

Answer:

The degree of r2 is 2. So, it is a quadratic polynomial.

(vii) 7x^{3}

Answer:

The degree of 7x^{3} is 3. So, it is a cubic polynomial.

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