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Question
The factors of x4 + x2 + 25 are
Options
(x2 + 3x + 5) (x2 − 3x + 5)
(x2 + 3x + 5) (x2 + 3x − 5)
(x2 + x +5) (x2 − x + 5)
none of these
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Solution
The given expression to be factorized is x4 + x2 + 25
This can be written in the form
`x^4 + x^2 + 25 = (x^2)^2+ 2.x^2 .5+ (5)^2 - 9x^2`
` = {(x^2)^2 + 2x^2 .5+ (5)^2 } - (3x)^2`
` = (x^2 + 5)^2 - (3x)^2`
` = (x^2 + 5)^2 - (3x)^2`
` = (x^2 + 5 + 3x)(x^2 + 5 - 3x)`
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