The sum of all possible values of a, for which the 4-digit number 547a is divisible by 3, is
7
15
10
13
A common factor of x4 - 256, x3 - 4x2 + 3x - 12 and x2 - 7x + 12 is
x + 4
x - 3
x - 4
x + 3
C.
x4 - 256 = 0⇒ x22 - 422 = 0⇒ x2 - 42x2 + 42 = 0⇒ x - 4x +4x2 + 42 = 0 ...iNow, x3 - 4x2 + 3x - 12 = 0⇒ x2x - 4 + 3x - 4 = 0⇒ x2 + 3x - 4 ...iiAnd, x2 - 7x + 12 = 0⇒ x2 - 7x + 12 = 0⇒ x2 - 4x - 3x + 12 = 0⇒ xx - 4 - 3x - 4 = 0⇒ x - 3x -4 = 0 ...iiiIn all the above eqs i, ii and iiix - 4 is the common factor