MCQ
The factors of x4 + x2 + 25 are:
- A(x2 + 3x + 5)(x2 - 3x + 5)
- B(x2 + 3x + 5)(x2 + 3x − 5)
- C(x2 + x +5)(x2 - x + 5)
- DNone of these.
✓
Answer
- (x2 + 3x + 5)(x2 - 3x + 5)
Solution:
For making perfect square to x4 + x2 + 25
We add +10x2 and -10x2 to it.
= x4 + x2 + 25
= x4 + x2 + 25 + 10x2 - 10x2
= [x4 + 10x2 + 25] - 9x2
= (x2 + 5)2 + (3x)2
= [(x2 + 5) + 3x][(x2 + 5) - 3x]
= (x2 + 3x + 5)(x2 - 3x + 5)
Hence, correct option is (a).
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