JAC Class 9 Maths Solutions Chapter 2 Polynomials Ex 2.1

Jharkhand Board JAC Class 9 Maths Solutions Chapter 2 Polynomials Ex 2.1 Textbook Exercise Questions and Answers.

JAC Board Class 9th Maths Solutions 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) 4x² – 3x + 7
(ii) y² + \( \sqrt{2} \)
(iii) 3\( \sqrt{t} \) + t\( \sqrt{2} \)
(iv) y + \(\frac{2}{y}\)
(v) x¹⁰ + y³ + t⁵⁰
Answer:
(i) 4x² – 3x + 7
There is only one variable x with whole number powers so this is a polynomial in one variable.

(ii) y² + \( \sqrt{2} \)
There is only one variable y with whole number powers so this is a polynomial in one variable.

(iii) 3\( \sqrt{t} \) + t\( \sqrt{2} \)
There is only one variable t but in 3\( \sqrt{t} \) power of t is \(\frac{1}{2}\) which is not a whole number. So, 3\( \sqrt{t} \) + t\( \sqrt{2} \) is not a polynomial.

(iv) y + \(\frac{2}{y}\)
There is only one variable y but \(\frac{2}{y}\) = 2y^-1 So, the power of y is not a whole number in the second term. Hence, y + \(\frac{2}{y}\) is not a polynomial.

(v) x¹⁰ + y³ + t⁵⁰
There are three variables x, y and t. So, this is not a polynomial in one variable.

Question 2.
Write the coefficients of x² in each of the following:
(i) 2 + x² + x
(ii) 2 – x² + x³
(iii) \(\frac{π}{2}\)x² + x
(iv) \( \sqrt{2} \) – 1
Answer:
(i) Coefficient of x² = 1
(ii) Coefficient of x² = -1
(iii) Coefficient of x² = \(\frac{π}{2}\)
(iv) Coefficient of x² = 0

Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Answer:
3x³⁵ + 7 and 4x¹⁰⁰ are binomials of degree 35 and monomial of degree 100 respectively.

Question 4.
Write the degree of each of the following polynomials:
(i) 5x³ + 4x² + 7x
(ii) 4 – y²
(iii) 5t – \( \sqrt{7} \)
(iv) 3
Answer:
(i) 5x³ has highest power in the given polynomial, which is 3. Therefore, degree of polynomial is 3.
(ii) -y² has highest power in the given polynomial, which is 2. Therefore, degree of polynomial is 2.
(iii) 5t has highest power in the given polynomial, which is 1. Therefore, degree of polynomial is 1.
(iv) There is no variable in the given polynomial. Therefore, degree of polynomial is 0.

Question 5.
Classify the following as linear, quadratic and cubic polynomials:
(i) x² + x
(ii) x – x³
(iii) y + y² + 4
(iv) 1 + x
(v) 3t
(vi) r²
(vii) 7x³
Answer:
(i) x² + x Quadratic Polynomial
(ii) x – x³ Cubic Polynomial
(iii) y + y² + 4 Quadratic Polynomial
(iv) 1 + x Linear Polynomial
(v) 3t Linear Polynomial
(vi) r² Quadratic Polynomial
(vii) 7x³ Cubic Polynomial