RBSE Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

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) 4x² – 3x + 7
Answer:
In 4x² – 3x + 7, all the exponents of x are whole numbers. So, it is a polynomial in one variable x.

(ii) y² + √2
Answer:
In y² + √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) x¹⁰ + y³ + t⁵⁰
Answer:
x¹⁰ + y³ + t⁵⁰ 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 x² in each of the following :
(i) 2 + x² + x
Answer:
Coefficient of x²: 1

(ii) 2 – x² + x³
Answer:
Coefficient of x²: – 1

(iii) \(\frac{π}{2}\)x² + x
Answer:
Coefficient of x²: \(\frac{π}{2}\)

(iv) √2x – 1
Answer:
Coefficient of x²: 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 5x³⁵ + 26x.
(ii) Monomial of degree 100 may be taken as 7x¹⁰⁰.

Question 4.
Write the degree of each of the following polynomials :
(i) 5x³ + 4x² + 7x
Answer:
The highest power term is 5×3 and its exponent is 3. So, its degree is 3.

(ii) 4 – y²
Answer:
The highest power term is – y² 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) x² + x
Answer:
The degree of x² + x is 2. So, it is a quadratic polynomial.

(ii) x – x³
Answer:
The degree of x – x³ is 3. So, it is a cubic polynomial.

(iii) y + y² + 4
Answer:
The degree of y + y² + 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) r²
Answer:
The degree of r2 is 2. So, it is a quadratic polynomial.

(vii) 7x³
Answer:
The degree of 7x³ is 3. So, it is a cubic polynomial.