MCQ
The expression $x^4 + 4$ can be factorized as:
- ✓$(x^2 + 2x + 2)(x^2 - 2x + 2)$
- B$(x^2 + 2x + 2)(x^2 + 2x - 2)$
- C$(x^2 - 2x - 2)(x^2- 2x + 2)$
- D$(x^2 + 2)(x^2 - 2)$
✓
Answer
Correct option: A.
$(x^2 + 2x + 2)(x^2 - 2x + 2)$
$x^4 + 4$
$= x^4 + 4 + 4x^2 - 4x^2$
$= (x^4 + 4x^2 + 4) - 4x^2$
$= (x^2 + 2)^2 - (2x)^2$
$= (x^2 + 2 - 2x)(x^2 + 2 + 2x)$
$= (x^2 + 2x + 2)(x^2 - 2x + 2)$
Hence, correct option is $ (a).$
$= x^4 + 4 + 4x^2 - 4x^2$
$= (x^4 + 4x^2 + 4) - 4x^2$
$= (x^2 + 2)^2 - (2x)^2$
$= (x^2 + 2 - 2x)(x^2 + 2 + 2x)$
$= (x^2 + 2x + 2)(x^2 - 2x + 2)$
Hence, correct option is $ (a).$
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