RD Sharma Solutions for Class 9 Chapter 6 Factorization of Polynomials Exercise 6.5

Chapter 6 Factorisation of Algebraic Expressions RD Sharma Solutions Exercise 6.5 Class 9 Maths

Chapter Name	RD Sharma Chapter 6 Factorisation of Polynomials Exercise 6.5
Book Name	RD Sharma Mathematics for Class 10
Other Exercises	Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4
Related Study	NCERT Solutions for Class 10 Maths

Exercise 6.5 Solutions

Using factor theorem, factorize each of the following polynomials : 

1. x³ + 6x² + 11x + 6

Solution

Let f(x) = x³ + 6x² + 11x + 6 be the given polynomial. 
The constant term in f(x) is 6 and factors of 6 are ±1, ±2, ±3 and ±6 
Putting x = -1 in f(x), we have 

2. x³ + 2x² - x - 2

Solution

Let f(x) = x³ + 2x² - x - 2
The constant term in f(x) is equal to -2 and factors of -2 and ±1, ±2
Putting x = 1 in f(x) , we have 

3. x³ - 6x² + 3x + 10 

Solution

4. x⁴ - 7x³ + 9x² + 7x - 10

Solution

5. x⁴ -2x³ - 7x² + 8x + 12

Solution 

6. x⁴ + 10x³ + 35x² + 50x + 24 

Solution

7. 2x⁴ - 7x³ - 13x² + 63x - 45

Solution

8. 3x³ - x³ - 3x + 1 

Solution

9. x³ - 23x² + 142x - 120 

Solution

10. y³ - 7y + 6

Solution

11. x³ - 10x² - 53x - 42

Solution

12. y³ - 2y² - 29y - 42

Solution

13. 2y³ - 5y² - 19y + 42

Solution

(y - 2)(y + 3)(2y - 7)

14. x³ + 13x² + 32x + 20

Solution

15. x³ - 3x² - 9x - 5

Solution

16. 2y³ + y² - 2y - 1

Solution

17. x³ - 2x² - x + 2

Solution

18. Factorize each of the following polynomials: 
(i) x³ + 13x² + 31x - 45 given that x + 9 is a factor 
(ii) 4x³ + 20x² + 33x + 18 given that 2x + 3 is a factor 

Solution