Question
Download Solution PDFThe factors of x4 + x2 + 25 are :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
(a + b)2 = a2 + b2 + 2ab
(a + b)(a - b) = a2 - b2
Calculation:
x4 + x2 + 25
It can be written as (x2)2 + 2 × x2 × 5 + (5)2 - (3x)2
⇒ x4 + 10x2 + 25 - 9x2
⇒ (x2 + 5)2 - (3x)2
⇒ (x2 + 5 + 3x)(x2 + 5 - 3x)
∴ The factors of x4 + x2 + 25 are (x2 + 3x + 5) (x2 - 3x + 5).
Last updated on Jun 13, 2025
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