NCERT Solutions for Class 10 Maths Exercise 2.3

NCERT Solutions for Class 10 Maths Exercise 2.3 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Class 10 Maths Polynomials Download as PDF

 NCERT Solutions for Class 10 Maths Polynomials

1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.

(i),

(ii),

(iii),

Ans. (i)

Therefore, quotient = x – 3 and Remainder = 7x – 9

(ii)

Therefore, quotient = and, Remainder = 8

(iii)

Therefore, quotient = and, Remainder = −5x + 10

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NCERT Solutions for Class 10 Maths Exercise 2.3

2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

(i)

(ii)

(iii)

Ans. (i)

Remainder = 0

Hence first polynomial is a factor of second polynomial.

(ii)

Remainder = 0

Hence first polynomial is a factor of second polynomial.

(iii)

Remainder ≠0

Hence first polynomial is not factor of second polynomial.

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NCERT Solutions for Class 10 Maths Exercise 2.3

3. Obtain all other zeroes of if two of its zeroes are and .

Ans. Two zeroes of are and which means that is a factor of .

Applying Division Algorithm to find more factors we get:

We have

⇒

= ()

= ()3

= 3()

= 3()(x+1)(x+1)

Therefore, other two zeroes of are −1 and −1.

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NCERT Solutions for Class 10 Maths Exercise 2.3

4. On dividing by a polynomial g(x), the quotient and remainder were (x-2) and (-2x+4) respectively. Find g(x).

Ans. Let, q(x) = (x – 2) and r(x) = (–2x+4)

According to Polynomial Division Algorithm, we have

p(x) = g(x).q(x) + r(x)

⇒ = g(x).(x−2)−2x+4

⇒ −4 = g(x).(x−2)

⇒ = g(x).(x−2)

⇒ g(x) =

So, Dividing by (x−2), we get

Therefore, we have g(x) =

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NCERT Solutions for Class 10 Maths Exercise 2.3

5. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

(i) deg p(x) = deg q(x)

(ii) deg q(x) = deg r(x)

(iii) deg r(x) = 0

Ans. (i) Let , g(x) = 3

So, we can see in this example that deg p(x) = deg q(x) = 2

(ii) Let and

We can see in this example that deg q(x) = deg r(x) = 1

(iii) Let, g(x) = x+3

We can see in this example that deg r(x) = 0

NCERT Solutions for Class 10 Maths Exercise 2.3

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