This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2. Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2 Equate each factor to zero to get the values of x x-1 = 0, x = 1 x +1 = 0, x = -1 x - 2 = 0, x = 2 substitute these value of x in the given equation \(ax^3 + bx^2\) + cx - 1 when x = 1 \(ax^3 + bx^2\) + cx - 1 = a + b + c - 1= 0 ------------------------(1) when x = -1 \(ax^3 + bx^2\) + cx - 1 = -a + b - c - 1 = 0-------------------------(2) when x = 2 \(ax^3 + bx^2\) + cx - 1 = 8a + 4b + 2c - 1 = 0 ----------------------(3) add equations 1 and 2 a + b + c - 1= 0 + -a + b - c - 1 = 0 b = 1 put b = 1 into equation (1) a + b + c - 1= 0 = a + 1 + c -1 = 0 a = - c put a = - c into equation(3) 8a + 4b + 2c - 1 = 0, -8c + 4 + 2c - 1 = 0 ( b = 1 remember) -6c = -3 c = \(\frac{-3}{-6}\) = \(\frac{1}{2}\) put c = \(\frac{1}{2}\) and b = 1 into equation (1) a + b + c - 1= 0 a + 1 + \(\frac{1}{2}\) - 1 = 0 a + \(\frac{1}{2}\) = 0 then a = \(\frac{-1}{2}\)