Let n is a positive integer greater than 7 and let f(x) is a biquadratic polynomial with 
and 
.Let 
and remainder when g(x) is divided by f(x) is 
then find the value of a b and c in terms of n
29using the given info...f(x) = (x-1)4
then (x+1)n = [λ(x)](x-1)4 + ax3 + bx2 + cx + d (where λ(x) is a function of x though we dont need to bother abt this function)...
replacing x-1 = t...we get..
(t+2)n = nC0 tn + nC1 tn-1.2 +......+ nCn-3 t3.2n-3 + nCn-2 t2.2n-2+ nCn-1 t.2n-1 + nCn.2n
so now nCn-3 t3.2n-3 + nCn-2 t2.2n-2+ nCn-1 t.2n-1 + nCn 2n = at3 + (3a + b)t2 + (3a + 2b + c)t + (a+ b+ c + d)
Now by comparing the L.H.S and R.H.S. we can get the value of a,b,c,d in terms of n... [1]
341We have
(x+1)^n = (x-1)^4 g(x) + A(x-1)^3 + B(x-1)^2 + C(x-1)+D
Put x=1 and we have D = 2^n
Differentiating once and putting x=1, we have
C= n2^{n-1}
In this manner we obtain B= n(n-1)2^{n-2}
and A= n(n-1)(n-3)2^{n-3}
Now to obtain a,b,c,d, we have a = A; b = -3A +B; c = 3A -2B+C; d = -A + B-C+D
