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Q.

What are the factors of x 3 − 1 x 3  ?

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a

x− 1 x x 2 − 1 x 2 +1   

b

x− 1 x x 2 + 1 x 2 −1  

c

x− 1 x x 2 + 1 x 2 +1  

d

x+ 1 x x 2 + 1 x 2 +1  

answer is B.

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Detailed Solution

The given polynomial is,
x 3 − 1 x 3  
We use the concept of algebraic identities to solve the given polynomial.
Apply the following identity:
a 3 − b 3 =(a−b)( a 2 +ab+ b 2 )  
Here, a=x   and b= 1 x .  
So,
We can expand the bracket as,
x 3 − 1 x 3 = x− 1 x x 2 + 1 x 2 +1  
Thus, the factors of x 3 − 1 x 3   are x− 1 x x 2 + 1 x 2 +1 .  
Hence, option 2 is the correct option.
 
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