NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.1 are provided here. These NCERT Maths solutions are prepared by our subject experts that make it easy for students to learn. The students can use it for reference while solving the exercise problems. The first exercise in NCERT Class 9 Maths Solutions Chapter 2, Polynomials – Exercise 2.1, discusses Polynomials in one or more variables.
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NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials Exercise 2.1
Access Answers to Maths NCERT Class 9 Chapter 2 – Polynomials Exercise 2.1
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:
The equation 4x2–3x+7 can be written as 4x2–3x1+7x0
Since x is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers, we can say that the expression 4x2–3x+7 is a polynomial in one variable.
(ii) y2+√2
Solution:
The equation y2+√2 can be written as y2+√2y0
Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers, we can say that the expression y2+√2 is a polynomial in one variable.
(iii) 3√t+t√2
Solution:
The equation 3√t+t√2 can be written as 3t1/2+√2t
Though t is the only variable in the given equation, the power of t (i.e.,1/2) is not a whole number. Hence, we can say that the expression 3√t+t√2 is not a polynomial in one variable.
(iv) y+2/y
Solution:
The equation y+2/y can be written as y+2y-1
Though y is the only variable in the given equation, the power of y (i.e.,-1) is not a whole number. Hence, we can say that the expression y+2/y is not a polynomial in one variable.
(v) x10+y3+t50
Solution:
Here, in the equation x10+y3+t50
Though powers 10, 3, and 50 are whole numbers, there are 3 variables used in the expression.
x10+y3+t50. Hence, it is not a polynomial in one variable.
2. Write the coefficients of x2 in each of the following.
(i) 2+x2+x
Solution:
The equation 2+x2+x can be written as 2+(1)x2+x
We know that the coefficient is the number which multiplies the variable.
Here, the number that multiplies the variable x2 is 1.
The coefficient of x2 in 2+x2+x is 1.
(ii) 2–x2+x3
Solution:
The equation 2–x2+x3 can be written as 2+(–1)x2+x3
We know that the coefficient is the number (along with its sign, i.e., – or +) which multiplies the variable.
Here, the number that multiplies the variable x2 is -1
The coefficient of x2 in 2–x2+x3 is -1.
(iii) (π/2)x2+x
Solution:
The equation (π/2)x2 +x can be written as (π/2)x2 + x
We know that the coefficient is the number (along with its sign, i.e., – or +) which multiplies the variable.
Here, the number that multiplies the variable x2 is π/2.
The coefficients of x2 in (π/2)x2 +x is π/2.
(iii)√2x-1
Solution:
The equation √2x-1 can be written as 0x2+√2x-1 [Since 0x2 is 0]
We know that the coefficient is the number (along with its sign, i.e., – or +) which multiplies the variable.
Here, the number that multiplies the variable x2 is 0.
The coefficient of x2 in √2x-1 is 0.
3. Give one example each of a binomial of degree 35 and of a monomial of degree 100.
Solution:
Binomial of degree 35: A polynomial having two terms and the highest degree of 35 is called a binomial of degree 35.
E.g., 3x35+5
Monomial of degree 100: A polynomial having one term and the highest degree of 100 is called a monomial of degree 100.
E.g., 4x100
4. Write the degree of each of the following polynomials.
(i) 5x3+4x2+7x
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, 5x3+4x2+7x = 5x3+4x2+7x1
The powers of the variable x are 3, 2, 1
The degree of 5x3+4x2+7x is 3, as 3 is the highest power of x in the equation.
(ii) 4–y2
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, in 4–y2,
The power of the variable y is 2.
The degree of 4–y2 is 2, as 2 is the highest power of y in the equation.
(iii) 5t–√7
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, in 5t–√7,
The power of the variable t is 1.
The degree of 5t–√7 is 1, as 1 is the highest power of y in the equation.
(iv) 3
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, 3 = 3×1 = 3× x0
The power of the variable here is 0.
The degree of 3 is 0.
5. Classify the following as linear, quadratic and cubic polynomials.
Solution:
We know that,
Linear polynomial: A polynomial of degree one is called a linear polynomial.
Quadratic polynomial: A polynomial of degree two is called a quadratic polynomial.
Cubic polynomial: A polynomial of degree three is called a cubic polynomial.
(i) x2+x
Solution:
The highest power of x2+x is 2
The degree is 2.
Hence, x2+x is a quadratic polynomial.
(ii) x–x3
Solution:
The highest power of x–x3 is 3.
The degree is 3.
Hence, x–x3 is a cubic polynomial.
(iii) y+y2+4
Solution:
The highest power of y+y2+4 is 2.
the degree is 2
Hence, y+y2+4is a quadratic polynomial
(iv) 1+x
Solution:
The highest power of 1+x is 1
The degree is 1.
Hence, 1+x is a linear polynomial.
(v) 3t
Solution:
The highest power of 3t is 1.
The degree is 1.
Hence, 3t is a linear polynomial.
(vi) r2
Solution:
The highest power of r2 is 2.
The degree is 2.
Hence, r2 is a quadratic polynomial.
(vii) 7x3
Solution:
The highest power of 7x3 is 3.
The degree is 3.
Hence, 7x3 is a cubic polynomial.
Access Other Exercise Solutions of Class 9 Maths Chapter 2 – Polynomials
Exercise 2.2 Solutions 4 Questions
Exercise 2.3 Solutions 3 Questions
Exercise 2.4 Solutions 5 Questions
Exercise 2.5 Solutions 16 Questions
Key Advantages of NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials Exercise 2.1
- The NCERT Class 9 Maths Solutions help students solve and revise all questions of Exercise 2.1.
- After going through the stepwise solutions given by our subject expert teachers, students will be able to get more marks.
- They help to do very well in Maths Board exams.
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