A common factor of x4 - 256, x3 - 4

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 Multiple Choice QuestionsMultiple Choice Questions

11.

The sum of all possible values of a, for which the 4-digit number 547a is divisible by 3, is

  • 7

  • 15

  • 10

  • 13


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12.

A common factor of x4 - 256, x3 - 4x2 +3x - 12 and x2 - 7x + 12 is

  • x + 4

  • x - 3

  • x - 4

  • x + 3


C.

x - 4

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


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