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· started a discussion

· 1 Months ago

Elaborate pls (Question:112002.0)

Elaborate

Question:
The factors of x8 + x4 + 1 are :
Options:
A) (x4+1-x2), (x2 + 1+x), (x2+1-x) 
B) (x4 + 1 - x2), (x2 - 1+x), (x2 + 1+x)
C) (x4 - 1 + x2), (x2 - 1+x), (x2 + 1+x)
D) (x4 - 1 + x2), (x2 + 1-x), (x2 + 1+x)
Solution:
Ans: (a)

x8 + x4 + 1 = (x4 + x2 + 1) (x4 - x2 + 1)

= (x4 - x2 + 1) (x2 + x + 1) (x2 - x + 1)

Pradnya Wasnik

· commented

· 1 Months ago

rewrite x^4 as 2x^4-x^4

you will get a perfect square
then solve using a^2-b^2

Yogesh Verma

· commented

· 1 Months ago

rewrite the middle term
x^8+x^4+1 = x^8+ 2 x^4 - x^4 +1
=> x^8 + 2 x^4 + 1 - x^4
=> (x^4 + 1)^2 - x^4
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