Q32
0. A common factor of x4 - 256, x3 - 4x2 + 3x - 12 and x2 - 7x + 12 is
- Option : C
- Explanation : x4 - 256 =0
=> (x2)2 - (42)2 = 0
=> (x2 - 42)(x2 - 42) = 0
=> (x - 4)(x + 4)(x2 + 42) = 0.....(i)
Now, x3 - 4x2 + 3x -12 = 0
=> x2 (x - 4) +3 (x - 4)=0
=> (x2 + 3)(x - 4) = 0 .....(ii)
And, x2 - 7x + 12=0
=> x2 - 4x - 3x +12=0
=> x(x - 4) -3(x - 4)=0
=> (x - 3)(x - 4) =0 ......(iii)
In all the above eqs.(i), (ii) and (iii) (x-4) is the common factor
