Question

Factorize: x⁴ + x² + 25

Answer 1

X4+x2+25 =(x4+10x2+25)-9x2 =(x2+5)^2-9x2 =(x2+5-3x)(x2+5+3x)

Answer 2

Answer:

$x^{4}+x^{2}+25=(x^{2}+3x+5)(x^{2}-3x+5)$

Step-by-step explanation:

$Given\: x^{4}+x^{2}+25$

$=x^{4}+10x^{2}-9x^{2}+25$

$=(x^{4}+10x^{2}+25)-9x^{2}$

$=[(x^{2})^{2}+2\times x^{2}+5^{2}]-(3x)^{2}$

$=\left(x^{2}+5\right)^{2}-(3x)^{2}$

$=[(x^{2}+5)+3x][(x^{2}+5)-3x]$

$=(x^{2}+3x+5)(x^{2}-3x+5)$

Therefore,

$x^{4}+x^{2}+25=(x^{2}+3x+5)(x^{2}-3x+5)$

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