Correct Answer: Option A
x2 - 11x + 30
= x2 - x(6 +5) + 30
= x2 -6x - 5x + 30
= x(x-6) - 5(x-6)
=(x-5)(x-6)
x3-4x2-2x-15
either (x-5) or (x-6) or both could be factors
inorder to factorize x3 - 4X2 - 2X - 15 WITH x - 5 ,
x - 5 = 0
=> x = 5
substituting x = 5 in the expression x3 - 4X2 - 2X - 15 we get,
(5)3 - 4(5)3 -2(5) -15 = 0
therefore x-5 is a factor of x3 - 4X2 - 2X - 15
following the same procedure with x-6 does not yeild zero and hence it is not a factor of x3 - 4X2 - 2X - 15
therefore Greatest Common Factor of the two expressions is (x-5)
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