The correct option is A 0
Given, f(x)=x3−6x2+ax+b is exactly divisible by
g(x)=x2−3x+2.
Let the remainder be r(x).
Then r(x)=0
x−3x2−3x+2 )¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ x3−6x2+ax+b −x3∓3x2±2x––––––––––––––––– −3x2+(a−2)x+b∓3x2±9x∓6–––––––––––––––––––––– (a−11)x+b+6
∴r(x)=(a−11)x+(b+6)
(a−11)x+(b+6)=0
The polynomial will be zero if
a−11=0 & b+6=0
∴a=11 & b=−6
∴12a+22b=12×11+22×(−6) =0