If 3 x^2+x+1 (x-1)^4 = a (x-1) + b (x-1)^2 + c (x-1)^3 + d (x-1)^4 then [ array ll a & b c & d array ] is equal to

Step-by-step solution

3 x^2+x+1 (x-1)^4 = a (x-1) + b (x-1)^2 + c (x-1)^3 + d (x-1)^4 3 x^2+x+1=a(x-1)^3+b(x-1)^2+c(x-1)+d3 x^2+x+1=a (x^3-1+3 x-3 x^2 )+b (x^2+1-2 x )+c(x-1)+d3 x^2+x+1=a x^3+(-3 a+b) x^2+(3 a-2 b+c) x+(-a+b-c+d) On comparing the coefficient of like powers of x on both sides. a=0,-3 a+b=3,3 a-2 b+c=2 b=3 0-6+c=1 c=7 and -a+b-c+d=1 0+3-7+d=1 d=5 Hence, [ array ll a & b c & d array ]= [ array ll 0 & 3 7 & 5 array ]