NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials
CBSE refers NCERT books to you in class 10 which is Board exams. For this purpose NCERT Solutions for polynomials Class 10 Maths is the best guide for you with detailed study material including the important topics. Those appearing for the board examinations can refer the NCERT Solutions for Class 10 Maths Chapter 2 while you are solving the questions from the textbook. Our solutions are important for you as you can get to know the answers to the questions in case you are not able to find it. It is also important for you to find all the solutions at one single place.
NCERT Solutions for polynomials Class 10 Maths Chapter 2 are provided which are prepared by our expert faculties to help you in board exam preparations. NCERT Solutions for polynomials Class 10 Maths help you to solve the problems easily and are prepared according to the CBSE syllabus and exam pattern so that you score good marks in exams. NCERT Solutions for polynomials Class 10 Maths provide a detailed and stepwise explanation of each answer to the questions given in the exercises of the Class 10 NCERT textbook and with Toppr app, you can download it for free.
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CBSE Class 10 Maths NCERT Solutions for Chapter 2 – Polynomials
NCERT Solutions for polynomials Class 10 explains the simplification and evaluation of polynomials, zeroes, and roots of a polynomial, evaluating zeros of polynomials by algebraically and graphically, relation of the roots of a quadratic and cubic equation with its coefficients, long division of polynomials. The chapter concludes with summarizing points that help you to revise the chapter and its concepts quickly.
Subtopics of Class 10 Maths Chapter 2 – Polynomials
- 2.1 – Introduction
- 2.2 – Geometrical Meaning of the Zeroes of a Polynomial
- 2.3 – Relationship between Zeroes and Coefficients of a Polynomial
- 2.4 – Division Algorithm for Polynomials
- 2.5 – Summary
Some Questions from NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials
Q.1 Write the coefficients of x2 in each of the following: (0)2 + x2+x (192-x2 + x2 (nuo 5×2+x (v) vāx-1
Solution
Coefficient of x2 in ax2 + bx+c = 0 is a.
Hence, coefficients of x
in
(0) 2 + x2 + x is 1
(ii) 2 – x2 + x3 is -1
que <x+x is
(iv) vēx-1 is o
Q.2. Give one example each of a binomial of degree 35 and of a monomial of degree 100.
Solution
Binomial of degree 35 may be taken as 435 + 4x And monomial of degree 100 may be taken as 5×100
Note: This question might have different answers.
Q.3. Write the degree of each of the following polynomials: (0) 5×3 + 4×2 + 7x (ii) 4 – 2 (ii) 5t-vi (iv) 3
Solution
(1) The power of the term is 5y3 and exponent is 3. So the degree is 3.
(ii) The power of the term is 72 and exponent is 2. So the degree is 2.
(iii) The power of the term is 5t and exponent is 1. So the degree is 1.
(iv) The only term here is 3 which can be written as 3yo and so the exponent is o or degree is 0.
Q.4. Classify the following as linear, quadratic and cubic polynomials: (1) x2 + x (ii) x-x? (lii) y+ y2 + 4 (iv) 1 + x
( 137 (vi) 2 (vii) 7x2
Solution
(0) The highest degree of y2 + x is 2, so it is a quadratic polynomial.
(ii) The highest degree of x- y3 is 3, so it is a cubic polynomial.
(iii) The highest degree of y + y2 + 4 is 2, so it is a quadratic polynomial.
(iv) The highest degree of x in (1 + x) is 1, so it is a linear polynomial.
(v)The highest degree of tin 3t is 1, so it is a linear polynomial.
(vi)The highest degree of 2 is 2, so it is a quadratic polynomial.
(vii) The highest degree of x in 7×3 is 3, so it is a cubic polynomial.
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Solved Questions for You
Question 1: Give one example each of a binomial of degree 35 and of a monomial of degree 100.
Answer: Binomial of degree 35 may be taken as x35+4x
And monomial of degree 100 may be taken as 5x100
Question 2: Write the degree of each of the following polynomials:
(i) 5x3+4x2+7x
(ii) 4−y2
(iii) 5t−7
(iv) 3
Answer: (i) The power of term is 5x3 and exponent is 3. So degree is 3.
(ii) The power of term is y2 and exponent is 2. So degree is 2.
(iii) The power of term is 5t and exponent is 1. So degree is 1.
(iv) The only term here is 3 which can be written as 3x0 and so exponent is 0 or degree is 0.
Question 3: Find the remainder when x3−ax2+6x−a is divided by x−a.
Answer: We have x3−ax2+6x−a
Apply remainder theorem
x−a=0
x=a
Put x=a in equation.
(a)3−a(a)2+6a−a
=a3−a3+6a−a
=6a−a
=5a
Then reminder is 5a
Question 4: 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) The highest degree of x2+x is 2, so it is a quadratic polynomials.
(ii) The highest degree of x−x3 is 3, so it is a cubic polynomials.
(iii)The highest degree of y+y2+4 is 2, so it is a quadratic polynomials.
(iv) The highest degree of x in (1+x) is 1, so it is a linear polynomials.
(v)The highest degree of t in 3t is 1, so it is a linear polynomials.
(vi)The highest degree of r2 is 2, so it is a quadratic polynomials
(vii)The highest degree of x in 7x3 is 3, so it is a cubic polynomials.
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