Quadratic eqn & remainder theroem

mx^3-3x^2+5x+4 & mx^3+4x-6 have common factor x-a. a is integer, find value of m. Ans: m=-1/4

x-a is a factor of mx^3-3x^2+5x+4
=> ma^3 - 3a^2 + 5a + 4 = 0...equation 1

x-a is a factor of mx^3+4x-6
=> ma^3 + 4a -6 = 0...equation 2

subtracting equation 2 from 1

we have -3a^2 +a + 10 = 0

=> 3a^2 - a - 10 = 0

=> 3a^2 -6a + 5a - 10 = 0

=> 3a(a-2) + 5(a-2) = 0

=> (3a+5)(a-2) = 0

=> a = 2, since a is an integer.

=> m(2)^3 + 4(2) - 6 =0 from equation 2

=> 8m = -2

=> m = -1/4