Answer :

Given, a pair of polynomial as 3x – 1, 3x3 – 10x2 + 9x – 2


Need to find out the first polynomial is factor of second and if not a factor need to find the remainder


To check 3x – 1 is a factor of 3x3 – 10x2 + 9x – 2 we must substitute x = in the second polynomial, we get as follows


3()3 – 10()2 + 9() – 2 = – 2


= – 3 – 2


= – 5


= 0


3x – 1 is not a factor


To find the remainder divide second polynomial by first polynomial


so, we can subtract a number from the second polynomial to get the remainder


3x3 – 10x2 + 9x – 2 = (3x – 1)q(x) + c


3x3 – 10x2 + 9x – 2 –c = (3x – 1)q(x)


c = ((3x3 – 10x2 + 9x – 2) – (3x – 1)) × q(x)


Now, substitute x = in the above equation we get



= – 2 – 0


c =


is the remainder


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