Factorize x^4+x^2+25
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1
Answer:
x
4
+x
2
+25
This can be written in the form,
⇒ (x
2
)
2
+2×x
2
×5+(5)
2
−9x
2
⇒ [(x
2
)
2
+2×x
2
×5+(5)
2
]−(3x)
2
⇒ (x
2
+5)
2
−(3x)
2
[ Since, a
2
+2ab+b
2
=(a+b)
2
]
⇒ (x
2
+5+3x)(x
2
+5−3x) [ Since, a
2
−b
2
=(a+b)(a−b) ]
∴ The factors of x
4
+x
2
+25 are (x
2
+5+3x)(x
2
+5−3x)
Step-by-step explanation:
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