PSEB 9th Class Maths Solutions Chapter 2 Polynomials Ex 2.1

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 2 Polynomials Ex 2.1 Textbook Exercise Questions and Answers.

PSEB Solutions for 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) 4x² – 3x + 7
Answer:
4x² – 3x + 7 is a polynomial in one variable, because in each term the exponent of variable x is a whole number.

(ii) y² + √2
Answer:
y² + √2 is a polynomial in one variable, because in each term the exponent of variable y is a whole number.

(iii) 3√t + t√2
Answer:
3√t + t√2 = \(3 t^{\frac{1}{2}}\) + √2t is not a polynomial in one variable, because the exponent of t in the first term is \(\frac{1}{2}\) which is not a whole number.

(iv) y + \(\frac{2}{y}\)
Answer:
y + \(\frac{2}{y}\) = y + 2y^-1 is not a polynomial in one variable, because the exponent of y in the second term is – 1 which is not a whole number.

(v) x¹⁰ + y³ + t⁵⁰
Answer:
x¹⁰ + y³ + t⁵⁰ is a polynomial, because the exponent of each of the variables x, y and t is a whole number, but it is not a polynomial in one variable.

Question 2.
Write the coefficients of x² in each of the following:
(i) 2 + x² + x
Answer:
In polynomial 2 + x² + x, the coefficient of x² is 1.

(ii) 2 – x² + x³
Answer:
In polynomial 2 – x² + x³, the coefficient of x² is – 1.

(iii) \(\frac{\pi}{2}\)x² + x
Answer:
In polynomial \(\frac{\pi}{2}\)x² + x, the coefficient of x² is \(\frac{\pi}{2}\).

(iv) √2x – 1
Answer:
In polynomial √2x – 1, the coefficient of x² is 0 as the term with x² is missing.

Question 3.
Give one example each of a binomial of degree 35 and of a monomial of degree 100.
Answer:
4x³⁵ – 2, √5 x³⁵ + 11, 7x³⁵ – √3 x are a few examples of a binomial of degree 35. Similarly, 7x¹⁰⁰, √2 x¹⁰⁰, 4π x¹⁰⁰ are a few examples of a monomial of degree 100.

Question 4.
Write the degree of each of the following polynomials:
(i) 5x³ + 4x² + 7x
Answer:
The degree of polynomial 5x³ + 4x² + 7x is 3.

(ii) 4 – y²
Answer:
The degree of polynomial 4 – y² is 2.

(iii) 5t – √7
Answer:
The degree of polynomial 5t – √7 is 1.

(iv) 3
Answer:
As the degree of constant polynomial 3 = 3x⁰ is 0.

Question 5.
Classify the following as and cubic polynomials:
(i) x² + x
Answer:
As the degree of polynomial x² + x is 2, it is a quadratic polynomial.

(ii) x – x³
Answer:
As the degree of polynomial x – x³ is 3 it is a cubic polynomial.

(iii) y + y² + 4
Answer:
As the degree of polynomial y + y² + 4 2. it is a quadratic polynomial.

(iv) 1 + x
Answer:
As the degree of polynomial 1 + x is 1, it is a linear polynomial.

(v) 3t
Answer:
As the degree of polynomial 3t is 1, it is a linear polynomial.

(vi) r²
Answer:
As the degree of polynomial r² is 2, it is a quadratic polynomial.

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