Solve: 2x^4 - 3x^3 - 24x^2 + 13x + 12 = 0
By inspection, x = 1 is a solution of 2x^4 - 3x^3 - 24x^2 + 13x + 12 = 0
Therefore, (x – 1) is a factor of 2x^4 - 3x^3 - 24x^2 + 13x + 12, giving
(x – 1)(2x^3 - x^2 – 25x – 12)
By inspection, x = 4 is a solution of 2x^3 - x^2 – 25x – 12 = 0
Therefore, (x – 4) is a factor of 2x^3 - x^2 – 25x – 12, giving
(x – 1)(x – 4)(2x^2 + 7x + 3)
The final quadratic factorises as: 2x^2 + 7x + 3 = (2x + 1)(x + 3)
The complete factorisation is: 2x^4 - 3x^3 - 24x^2 + 13x + 12 = (x – 1)(x – 4)(2x + 1)(x + 3) = 0
Solution is: x = 1, x = 4, x = -1/2, x = -3