## NCERT solutions for class 10 Maths

**Chapter 2**

## Polynomials

**Exercise 2.3**

**Ex 2.3 Question 1.**

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

**(i) p(x) = x ^{3} – 3x^{2} + 5x – 3, g(x) = x^{2} – 2**

**(ii) p(x) = x**

^{4}– 3x^{2}+ 4x + 5, g(x) = x^{2}+ 1 – x**(iii) p(x) = x**

^{4}– 5x + 6, g(x) = 2 – x^{2 Solution:}**Ex 2.3 Question 2.**

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

**(i) t ^{2} – 3, 2t^{4} + 3t^{3} – 2t^{2}– 9t – 12**

**(ii) x**

^{2}+ 3x + 1, 3x^{4}+ 5x^{3}– 7x^{2}+ 2x + 2**(iii) x**

^{2}+ 3x + 1, x^{5}– 4x^{3 }+ x^{2}+ 3x + 1**Solution:**

**Ex 2.3 Question 3.**

**Obtain all other zeroes of 3x ^{4}+6x^{3}-2x^{2}-10x-5, if two of its zeroes are √(5/3) and – √(5/3).**

**Solution:**

**Ex 2.3 Question 4.**

**On dividing x ^{3 }– 3x^{2} + x + 2bya polynomial g(x), the quotient and remainder were x – 2 and -2x + 4 respectively. Find g(x).**

**Solution:**

**Ex 2.3 Question 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**

**Solution:**