Chapter 6 Factorisation of Algebraic Expressions RD Sharma Solutions Exercise 6.3 Class 9 Maths

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

  • Exercise 6.1
  • Exercise 6.2
  • Exercise 6.4
  • Exercise 6.5

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) = x3 + 4x2 - 3x + 10, g(x) = x + 4

Solution

We have f(x) = x3 + 4x2 - 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) = 4x4 - 3x3 - 2x2 + x - 7, g(x) = x - 1

Solution

We have, 
f(x) = 4x4 - 3x3 - 2x2 + 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)


3. f(x) = 2x4 - 6x3 + 2x2 - x + 2, g(x) = x + 2
Solution
We have, 
f(x) = 2x4 - 6x3 + 2x2 - x + 2, and  g(x) = x + 2 
Therefore, by remainder theorem when f(x) is divide by g(x) = x - (-2), the remainder is equal to f(-2) 

4. f(x) = 4x3 - 12x3 + 14x - 3, g(x) = 2x - 1 
Solution
We have 
f(x) = 4x3 - 12x3 + 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) = x3 - 6x3 + 2x - 4, g(x) = 1 - 2x
Solution
We have 
f(x) = x3 - 6x3 + 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) 

6. f(x) = x3 - 3x3 + 4, g(x) = x - 2
Solution 
We have 
f(x) = x3 - 3x3 + 4, and g(x) = x - 2
Therefore, by remainder theorem when f(x) is divided by g(x) = x - 2, the remainder is equal to f(2)

7. f(x) = 9x3 - 3x3 + x - 5, g(x) = x - 2/3
Solution
We have 
f(x) = 9x3 - 3x3 + 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) 

8. f(x) = 3x3 + 2x3 - x3/3 - x/9 + 2/27, g(x) = x+ 2/3 
Solution
We have, 

9. If the polynomials 2x3 + ax2 + 3x - 5 and x3 + x2 -4x + a leave the same remainder when divided by x - 2, find the value of a.
Solution
Let p(x) = 2x3 + ax2 + 3x - 5 and q(x) = x3 + x2 - 4x + a be the given polynomials 
The remainders when p(x) and q(x) are divided by (x - 2) are p(2) and q(2) respectively. 
By the given condition we have 

10. The polynomials ax3 + 3x2 - 3 and 2x3 - 5x + a when divided by (x - 4) leave the remainder R1 and R2 respectively. Find the values of a in each of the following cases, if 
(i) R1 = R2
(ii) R1 + R2 = 0
(iii) 2R1 + R2 = 0
Solution

11. If the polynomials ax3 + 3x2 - 13 and 2x3 - 5x + a, when divided by (x - 2) leave the same remainder, find the value of a.
Solution
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