NCERT Solutions Class 9th Maths 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

Solution – We have 4x² – 3x + 7 = 4x² – 3x + 7x⁰
It is a polynomial in one variable i.e., x
because each exponent of x is a whole number.

(ii) y² + √2

Solution – We have y² + √2 = y² + √2y⁰
It is a polynomial in one variable i.e., y
because each exponent of y is a whole number.

(iii) 3 √t + t√2

Solution – We have 3 √t + t√2 = 3 √t^1/2 + √2.t
It is not a polynomial, because one of the exponents of t is 1/2,
which is not a whole number.

(iv) y+ 2/y

Solution – We have y + y+2/y = y + 2/y^-1
It is not a polynomial, because one of the exponents of y is -1,
which is not a whole number.

(v) x¹⁰+ y³+t⁵⁰

Solution – We have x¹⁰+  y³ + t⁵⁰
Here, exponent of every variable is a whole number,
but x¹⁰ + y³ + t⁵⁰ is a polynomial in x, y and t, i.e., in three variables.
So, it is not a polynomial in one variable.

Question 2. Write the coefficients of x² in each of the following:

(i) 2 + x² + x

Solution
The given polynomial is 2 + x² + x.
The coefficient of x² is 1.

(ii) 2 – x² + x³

Solution
The given polynomial is 2 – x² + x³.
The coefficient of x² is -1.

(iii) π/2 x² + x

Solution
The given polynomial is π/2x2 + x.
The coefficient of x² is π/2.

(iv) √2x – 1

Solution
The given polynomial is √2 x – 1.
The coefficient of x² is 0.

Question 3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Solution
(i) A binomial of degree 35 can be 3x³⁵ -4.
(ii) A monomial of degree 100 can be √2y¹⁰⁰.

Question 4. Write the degree of each of the following polynomials.

(i) 5x³+4x² + 7x

Solution
The given polynomial is 5x³ + 4x² + 7x.
The highest power of the variable x is 3.
So, the degree of the polynomial is 3.

(ii) 4 – y²

Solution
The given polynomial is 4- y². The highest
power of the variable y is 2.
So, the degree of the polynomial is 2.

(iii) 5t – √7

Solution
The given polynomial is 5t – √7 .
The highest power of variable t is 1.
So, the degree of the polynomial is 1.

(iv) 3

Solution
Since, 3 = 3x° [∵ x°=1]
So, the degree of the polynomial is 0.

Question 5. Classify the following as linear, quadratic and cubic polynomials.

(i) x²+ x

Solution
The degree of x² + x is 2. So, it is a quadratic polynomial.

(ii) x – x³

Solution
The degree of x – x³ is 3. So, it is a cubic polynomial.

(iii) y + y²+4

Solution
The degree of y + y² + 4 is 2. So, it is a quadratic polynomial.

(iv) 1 + x

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

(v) 3t

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

(vi) r²

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

(vii) 7x³

Solution
The degree of 7x³ is 3. So, it is a cubic polynomial.