Chapter 6 Factorisation of Algebraic Expressions RD Sharma Solutions Exercise 6.3 Class 9 Maths
Chapter Name  RD Sharma Chapter 6 Factorisation of Polynomials Exercise 6.3 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 6.3 Solutions
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)
1. f(x) = x^{3} + 4x^{2}  3x + 10, g(x) = x + 4
Solution
We have f(x) = x^{3} + 4x^{2}  3x + 10, g(x) = x + 4
Therefore, by remainder theorem when f(x) is divided by g(x) = x  ( 4), the remainder is equal to f(4)
2. f(x) = 4x^{4}  3x^{3}  2x^{2} + x  7, g(x) = x  1
Solution
We have,
f(x) = 4x^{4}  3x^{3}  2x^{2} + x  7, and g(x) = x  1
Therefore by remainder theorem when f(x) is divide by g(x) = x  1, the remainder is equal to f(+1)
Solution
f(x) = 4x^{3}  12x^{3} + 14x  3, and g(x) = 2x  1
Therefore, by remainder theorem when f(x) is divide by g(x) = 2[x  1/2], the remainder is equal to f(1/2)
5. f(x) = x^{3}  6x^{3} + 2x  4, g(x) = 1  2x
f(x) = x^{3}  6x^{3} + 2x  4, and g(x) = 1  2x
Therefore, by remainder theorem when f(x) is divided by g(x) = 2(x  1/2), the remainder is equal to f(1/2)
7. f(x) = 9x^{3}  3x^{3} + x  5, g(x) = x  2/3
f(x) = 9x^{3}  3x^{3} + x  5, and g(x) = x  2/3
Therefore, by remainder theorem when f(x) is divided by g(x) = x  2/3, the remainder is equal to f(2/3)
The remainders when p(x) and q(x) are divided by (x  2) are p(2) and q(2) respectively.
10. The polynomials ax^{3} + 3x^{2}  3 and 2x^{3}  5x + a when divided by (x  4) leave the remainder R_{1} and R_{2} respectively. Find the values of a in each of the following cases, if