MCQ
The expression $x^4+4$ can be factorized as:
- A$\left(x^2-2 x-2\right)\left(x^2-2 x+2\right)$
- B$\left(x^2+2\right)\left(x^2-2\right)$
- C$\left(x^2+2 x+2\right)\left(x^2+2 x-2\right)$
- ✓$\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
✓
Answer
Correct option: D.
$\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
The given expression to be factorized is $x^4+4$This can be written in the form
$x^4+4=\left(x^2\right)^2+(2)^2+4 x^2-4 x^2$
$=\{(x^2)^2+2 \times x^2 \times 2+(2)^2\}-(2 x)^2$
$=\left(x^2+2\right)^2-(2 x)^2$
$=\left(x^2+2+2 x\right)\left(x^2+2-2 x\right)$
$x^4+4=\left(x^2\right)^2+(2)^2+4 x^2-4 x^2$
$=\{(x^2)^2+2 \times x^2 \times 2+(2)^2\}-(2 x)^2$
$=\left(x^2+2\right)^2-(2 x)^2$
$=\left(x^2+2+2 x\right)\left(x^2+2-2 x\right)$
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