Answer :

Given, a pair of polynomial as 2x – 1, 3x3 – x2 – 8x + 6


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


To check 2x – 1 is a factor of 3x3 – x2 – 8x + 6 we must substitute x = in the second polynomial, we get as follows


3()3 – ()2 – 8() + 6 = + 6 = + 6 = + 2 = 0


2x – 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 – x2 – 8x + 6 = (2x – 1)q(x) + c


3x3 – x2 – 8x + 6 –c = (2x – 1)q(x)


c = ((3x3 – x2 – 8x + 6) – (2x – 1)) × q(x)


Now, substitute x = in the above equation we get


c = (3()3 – ()2 – 8() + 6 – 2() + 1) × q(1)


= + 6


c =


is the remainder


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