14. Factorisation – Class 8 Mathematics NCERT Chapter 14 Complete Guide (CBSE)

NCERT Class 8 Mathematics Chapter 14: Factorisation – All Exercise Solutions | CBSE Board

Chapter 14: Factorisation

             Exercise 14.1

1. Find the common factors of the given terms.
(i)         (ii)       (iii)        (iv)     (v)     (vi)       (vii)     (viii)

Solution: (i) We have,   and  

The common factor of  and is  

(ii)

We have,    and

The common factor of and  is

(iii)

We have,   and 

The common factor of and  is
(iv)

We have,    ,    and  

The common factor of  and is 2 .

(v) 

We have,

 

 

The common factor of  and  is  .
(vi)  

We have,

 

 

The common factor of   and  is

(vii)

We have,

 

  and

The common factor of and  is

(viii)

We have,

The common factor of and  is

2. Factorise the following expressions.
(i)        (ii)         (iii)       (iv)      (v)      (vi)   

(vii)       (viii)       (ix)         (x) 

Solution: (i) We have,   

(ii) We have,    

(iii) We have,   
(iv) We have,               

(v) We have,   
(vi) We have,             

(vii) We have,   
(viii) We have,        

(ix) We have,    
(x) We have,   

3. Factorise.
(i)        (ii)         (iii)         (iv)         (v)  

Solution: (i) We have.       

(ii) We have,          

(iii) We have,    

(iv) We have,                

(v) We have,     

                       Exercise 14.2

1. Factorise the following expressions.
(i)            (ii)          (iii)     

(iv)    (v)       (vi)   

(vii)  (Hint: Expand  first)        (viii)  

Solution: (i) We have,

            

(ii) We have, 

         

(iii) We have, 

  
(iv) We have,

   

(v) We have,   

  
(vi) We have,

  
(vii) We have,

      

(viii) We have,

  

2. Factorise.
(i)        (ii)            (iii)        (iv)       (v)     (vi)                 (vii)        (viii)

Solution: (i) We have, 

             

(ii) We have, 

              

(iii) We have,

   
(iv) We have,

             

(v) We have,

   
(vi) We have,

               

(vii) We have,

 
(viii) We have,

  

3. Factorise the expressions.
(i)            (ii)         (iii)     (iv)       (v)    

 (vi)       (vii)    (viii)  (ix)

Solution: (i) We have,            

(ii) We have,        

(iii) We have,
(iv) We have,

           

(v) We have,

 
(vi) We have,               

(vii) We have,

  

(viii) We have,

 

(ix) We have,

   

4. Factorise.
(i)            (ii)         (iii)         (iv)           (v)   

Solution: (i) We have,         

(ii) We have,  

      

(iii) We have,

 

 
(iv) We have,     

   

(v) We have,

  

5. Factorise the following expressions.
(i)         (ii)     (iii)

Solution: (i)We have,

        

(ii) We have,             

(iii) We have,      

                        Exercise 14.3

1. Carry out the following divisions.
(i)      (ii)   (iii)    (iv)     (v)

Solution: (i) We have,   

(ii) We have,  

(iii)  We have,     

(iv) We have,    

(v) We have,   

2. Divide the given polynomial by the given monomial.
(i)       (ii)     (iii)    (iv)      (v)

Solution: (i) We have,  

(ii) We have,         

(iii) We have,

  

(iv) We have, 

 

(v) We have,   

3. Work out the following divisions.
(i)       (ii)        (iii)     

(iv)    (v)

Solution: (i) We have,              

(ii) We have,   

(iii) We have,        

(iv) We have,

    

(v) We have,

    

4. Divide as directed.
(i)       (ii)    

(iii)     

(iv)       (v) 

Solution:  (i) We have,

     

(ii) We have,

   

(iii) We have,  

  

(iv) We have,

    

(v) We have,

 

5. Factorise the expressions and divide them as directed.
(i)       (ii)     (iii)     (iv)    

(v)    (vi)     (vii)   

Solution:  (i) We have,

  

(ii)  We have,

       

(iii) We have,

       

(iv) We have,

      

(v) We have,

  

 (vi) We have,

       

(vii) We have,

     

                        Exercise 14.4

Find and correct the errors in the following mathematical statements.
1.                  2.                 3.     

4.                    5.              6.           7.                      

8.        9.  

10. Substituting  in
(a)  gives
(b)  gives
(c)  gives
11.                  12.     13.                 14.
15.       16.                17.              18.              19.              20.        21. 

Solution:  1. The given statement is:   

Correct statement:  

2.  The given statement is:   

Correct statement is: 

3.  The given statement is :  

Correct statement is:   

4.  The given statement is:  

Correct statement is:  

5.  The given statement is :    

Correct statement is:     

6.   The given statement is:  

Correct statement is:  
7.  The given statement is :                       

Correct statement is:                       

8. The given statement is :

Correct statement is:  
9. The given statement is :

Correct statement is:  

10. Substituting  in
 (a)   gives  

The given statement is :   

Correct statement is:  

(b)  x²-5x+4 gives  

The given statement is :  gives  

Correct statement is:   

(c)  gives  

The given statement is:   gives

Correct statement is:   

11.  The given statement is :                   

Correct statement is:                   

12.  The given statement is:  

Correct statement is:  

13.  The given statement is:     

Correct statement is:   

14.  The given statement is :   

Correct statement is:   

15. The given statement is:         

Correct statement is:       

16.  The given statement is :  

Correct statement is:   

17.  The given statement is :  

Correct statement is: 

18.   The given statement is :  

Correct statement is:  

19.  The given statement is  

Correct statement is:   

20. The given statement is 

Correct statement is:  

21.   The given statement is  

Correct statement is:  

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