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

**Exercise 6.3**

1.Â 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: (1âˆ’8).

(i) f(x) =x

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

**2.Â f(x) = 4x**

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

**Solution**

3.Â f(x) = 2x

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

4.Â f(x) = 4x

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

5.Â f(x) =Â x

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

**6.Â f(x) =Â x**

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

**7.Â f(x) = 9x**

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

**Solution**

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

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

**Solution**

**9. If the polynomials 2x**

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

**10.Â 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}Â respectively. Find the value of a in each of the following cases, if**(a) R**

_{1}Â = R_{2}Â**(b)Â R**

_{1}+R_{2}Â =0**(c) 2R**

_{1}Â -R_{2}Â =0**Solution**

**11.Â If the polynomials ax**

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

**Solution**

**Solution**