Question

if the polynomial ax^3 +4x^2+3x-4 and ,x^3-4x+a leaves the same remainder when divided by x+3 ,find the value of a

Answer 1

     p(x 1)  = ax^3 + 4 x^2 +3 x - 4
p(x 1= -3) = a (-3)^3 + 4 (-3)^2 + 3 (-3) - 4
                = -27 a + 36 -9 -4
                =  -27 a + 23  --------------------------------(1)
       p(x 2) = x^3 - 4 x + a
p(x 2 = -3) = (-3)^3 - 4 (-3) + a
                  = -27 + 12 + a
                  = -15 + a ------------------------------------(2)
equation (1) & (2) are equal
so,        p(x 1) = p(x 2)
      -27 a + 23 = -15 + a
       - 27 a - a  =  -15 -23
          -28 a     = -38
                  a = 38/28 = 19/14