We have to find the remainder when f=3x^4-2x^3+x^2+ax-1 is divided by (x-1)^2

(x-1)^2

=> x^2 - 2x + 1

We use long division to divide 3x^4-2x^3+x^2+ax-1 by x^2 - 2x + 1.

x^2 - 2x + 1 | 3x^4-2x^3+x^2+ax-1 | 3x^2 + 4x+6

......................3x^4-6x^3+3x^2

...................-----------------------------

..............................4x^3 - 2x^2 +ax - 1

..............................4x^3 - 8x^2 + 4x

----------------------------------------------

........................................6x^2 +(a-4)x - 1

........................................6x^2 - 12x + 6

-----------------------------------------------

.................................................. +(a + 8)x - 7

**Therefore the remainder is (a+8)x -7**.

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