b. Factorise : x^8 + x^4 + 1
Answers
Answered by
1
Step-by-step explanation:
8
+x
4
+1
=(x
4
)
2
+(1)
2
+x
4
=(x
4
+1)
2
−2x
4
+x
4
=(x
4
+1)
2
−(x
2
)
2
=(x
4
+1+x
2
)(x
4
+1−x
2
)
=[(x
2
)
2
+(1)
2
+x
2
][x
4
−x
2
+1]
=[(x
2
+1)
2
−2x
2
+x
2
][x
4
−x
2
+1]
=[(x
2
+1)
2
−(x)
2
][x
4
−x
2
+1]
=(x
2
+1+x)(x
2
+1−x)((x
4
−x
2
+1)
=(x
2
+x+1)(x
2
−x+1)(x
4
−x
2
+1)
Answered by
2
Answer:
The factor of x^8 + x^4 + 1...
The factor of x
8
+x
4
+1 are:
ANSWER
x
8
+x
4
+1
=(x
4
)
2
+(1)
2
+x
4
=(x
4
+1)
2
−2x
4
+x
4
=(x
4
+1)
2
−(x
2
)
2
=(x
4
+1+x
2
)(x
4
+1−x
2
)
=[(x
2
)
2
+(1)
2
+x
2
][x
4
−x
2
+1]
=[(x
2
+1)
2
−2x
2
+x
2
][x
4
−x
2
+1]
=[(x
2
+1)
2
−(x)
2
][x
4
−x
2
+1]
=(x
2
+1+x)(x
2
+1−x)((x
4
−x
2
+1)
=(x
2
+x+1)(x
2
−x+1)(x
4
−x
2
+1)
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