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Q.

[[1]] is the factor of x4−x2−12.


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Detailed Solution

Given, x4−x2−12
Assume x2 = t equation will be
 ⇒t2−t−12
 split -1 in such that multiplication of 2 terms will be equal to -12
⇒t2−4t+3t−12
Taking common t and 3
⇒t(t−4)+3(t−4)
Now taking common (t−4)
⇒(t−4)(t+3)
Then substitute x2 = t
⇒(x2−4)(x2+3)
It is known that (a2−b2) = (a−b)(a+b) then (x2−4) = (x−2)(x+2)
⇒(x−2)(x+2)(x2+3)
 
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