Question
Factorize:
$x^4 + x^2 + 25.$
$x^4 + x^2 + 25.$
✓
Answer
The given expression to be factorized is $x^4 + x^2 + 25$
This can be written in the form
$x^4 + x^2 + 25 = (x^2)^2 + 2.x^2.5 + (5)^2 - 9x^2$
$= {(x^2)^2 + 2.x^2.5 + (5)^2} - (3x)^2$
$= (x^2 + 5)^2 - (3x)^2$
$= (x^2 + 5 + 3x)(x^2 + 5 - 3x)$
We cannot further factorize the expression.
So, the required factorization is $x^4 + x^2 + 25 = (x^2 + 5 + 3x)(x^2 + 5 - 3x).$
This can be written in the form
$x^4 + x^2 + 25 = (x^2)^2 + 2.x^2.5 + (5)^2 - 9x^2$
$= {(x^2)^2 + 2.x^2.5 + (5)^2} - (3x)^2$
$= (x^2 + 5)^2 - (3x)^2$
$= (x^2 + 5 + 3x)(x^2 + 5 - 3x)$
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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