Question

the polynomials ax^3+bx^2+x-6has( x+2) as a factor and leaves remainder 4 . when divided by x-2 find a and b

Answer 1

     P(x) = ax^3 + bx^2 + x - 6
p(x=-2) = a (-2)^3 + b (-2)^2 -2 -6
        0   = -8 a  + 4 b -8  (since it is a factor p(x)=0 )
      -8 a + 4 b  = 8 ---------------------------------------------------(1)
     P(x) = ax^3 + bx^2 + x - 6
p(x = 2) =  a (2)^3 + b (2)^2 +2 -6
        4   = 8 a + 4 b -4
        8 a + 4 b = 8 -------------------------------------------------(2)
solving equation 1 & 2
(1) + (2) =>  8 b = 16  ,  b = 2
(1) - (2)  =>  -16 a = 0 , a = 0

so Answer is a=0 & b=2