Answer :

If (x - 2) is a factor of the polynomial (x3 + mx2 – x + 6) then it must satisfy it.

So, putting x = 2 the polynomial must be zero.


Putting x = 2 and equating to zero.


= (23 + m22 –2 + 6)


= 4m + 12 = 0


= m = -3


If we divide f(x) = (x3 + mx2 –x + 6) by (x - 3) remainder can be find at value of –


(x - 3) = 0


Or x = 3


So we will put x = 3 in f(x) = (x3 + mx2 – x + 6)


f(3) = (33 + m32 – 3 + 6)


= 30 + 9m


So remainder = 30 + 9m


= 30 + 9(-3) = 30 - 27 = 3


So, r = 3.


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