Factors of x⁴ + x² + 25
The factors of \[ x^4+x^2+25 \] are
(a) \((x^2+3x+5)(x^2-3x+5)\)
(b) \((x^2+3x+5)(x^2+3x-5)\)
(c) \((x^2+x+5)(x^2-x+5)\)
(d) none of these
Solution
\[ x^4+x^2+25 \]
\[ =x^4+10x^2+25-9x^2 \]
\[ =(x^2+5)^2-(3x)^2 \]
\[ =(x^2+5+3x)(x^2+5-3x) \]
\[ =(x^2+3x+5)(x^2-3x+5) \]
Therefore,
\[ \boxed{(a)\ (x^2+3x+5)(x^2-3x+5)} \]