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Q.

What are the factors of x 4 −625  ?


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a

x 2 +25 x+5 x+5  

b

x 2 +25 x−5 x+5  

c

x 2 −25 x−5 x+5  

d

x 2 +25 x−5 x−5   

answer is B.

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Detailed Solution

The given expression is x 4 −625  .
Express the given expression x 4 −625   in terms of a and b.
Here, a= x 2   and b= 25 2   .
Substitute the value of a and b respectively and use the difference of squares. x 2 2 − 25 2 = x 2 −25 x 2 +25  
Rewrite x 2 −25   in the form of Question Image, here x 2 +25   cannot be further factorized. Thus, a=x and b=5.
x 4 −625= x 2 − 5 2 ⇒ x−5 x+5  
Combine all the factors together.
x 4 −625= x 2 −25 x 2 +25 ⇒ x 2 +25 x−5 x+5  
Therefore, the factors of x 4 −625   are x 2 +25 x−5 x+5  .
Thus, option 2 is correct.
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