x2-11x+30 এবংx3-4x2-2x-15 . এর গ.সা.গু কত?

A    x-5

B    x-6

C    x2+x+3

D    x2-x+3

Solution

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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