The factors of X4 + X2 + 25 are:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. (X2 + 3X + 5) (X2 - 3X + 5).
Formula used:
(a + b)2 = a2 + b2 + 2ab ----- (1)
(a + b)(a - b) = a2 - b2 ----- (2)
Calculation:
x4 + x2 + 25
It can be written as
⇒ (x2)2 + 2 × x2 × 5 + (5)2 - (3x)2
⇒ (x2 + 5)2 - (3x)2
Using equation (2), we get
⇒ (x2 + 3x + 5)(x2 - 3x + 5)