#### Chapter 6 Factorization of Polynomials R.D. Sharma Solutions for Class 9th Math Exercise 6.3

**Exercise 6.3**

1. In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8).

(i) f(x) =x

^{3}+4x^{2}-3x+10, g(x) = x+4**Solution**

**2. f(x) = 4x**

^{4}-3x^{3}-2x^{2}+x-7, g(x) = x-1

**Solution**

3. f(x) = 2x

^{4}-6x^{3}+2x^{2}-x+2, g(x) = x+2**Solution**

4. f(x) = 4x

^{2}-12x^{2}+14x-3, g(x) = 2x-1**Solution**

5. f(x) = x

^{3}-6x^{2}+2x-4, g(x) = 1-2x**Solution**

**6. f(x) = x**

^{4}-3x^{2}+4, g(x) = x-2**Solution**

**7. f(x) = 9x**

^{3}-3x^{2}+x-5, g(x) = x - 2/3

**Solution**

**8. f(x) = 3x**

^{4}+2x^{3}- x^{2}/3 - x/9 + 2/27, g(x) = x + 2/3

**Solution**

**9. If the polynomials 2x**

^{3}+ax^{2}+3x-5 and x^{3}+x^{2}-4x+a leave the same remainder when divided by x-2, find the value of a.**Solution**

**10. The polynomials ax**

^{3}+3x^{2}-3 and 2x^{3}+5x+a when divided by (x-4) leave the remainders R_{1}and R_{2}respectively. Find the value of a in each of the following cases, if**(a) R**

_{1}= R_{2}**(b) R**

_{1}+R_{2}=0**(c) 2R**

_{1}-R_{2}=0**Solution**

**11. If the polynomials ax**

^{3}+3x^{2}- 13 and 2x^{3}-5x+a, when divided by (x-2) leave the same remainder, find the value of a.

**Solution**

**Solution**