Factorization of x⁴ + 4
The expression \[ x^4+4 \] can be factorized as
(a) \((x^2+2x+2)(x^2-2x+2)\)
(b) \((x^2+2x+2)(x^2+2x-2)\)
(c) \((x^2-2x-2)(x^2-2x+2)\)
(d) \((x^2+2)(x^2-2)\)
Solution
\[ x^4+4 \]
\[ =x^4+4x^2+4-4x^2 \]
\[ =(x^2+2)^2-(2x)^2 \]
\[ =(x^2+2x+2)(x^2-2x+2) \]
Therefore,
\[ \boxed{(a)\ (x^2+2x+2)(x^2-2x+2)} \]