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प्रश्न
Factorize: x4 + x2 + 25.
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उत्तर
The given expression to be factorized is x4 + x2 + 25
This can be written in the form
x4 + x2 + 25= ` (x^2)^2 + 2x^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 + 3x) (x^2 + 5 - 3x)`
We cannot further factorize the expression.
So, the required factorization is. `x^4 + x^2 + 25 = (x^2 + 5+3x)(x^2 + 5 - 3x)`
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