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Question
The expression x4 + 4 can be factorized as
Options
(x2 + 2x + 2) (x2 − 2x + 2)
(x2 + 2x + 2) (x2 + 2x + 2)
(x2 − 2x − 2) (x2 − 2x + 2)
(x2 + 2) (x2 − 2)
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Solution
The given expression to be factorized is x4 + 4
This can be written in the form
x4 + 4 =` (x^2)^2 + (2)^2 + 2x^2 2.- 4x^2`
` = {(x^2)^2 +2.x^2 . 2+ (2)^2} - (2x)^2`
` = (x^2 +2)^2 - (2x)^2`
` = (x^2 + 2 + 2x)(x^2 +2 -2x)`
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