Solve the equation 2x^3 - 5x^2 - 4x + 3 = 0.

In order to answer this question, the expression on the left side of the equation needs to be factorised. This can be done in three stages. 1) finding a factor by subbing in common integers (0, +/- 1, +/-2, +/-3) until the equation outputs a 0. 2) polynomial division by using the 'bus stop' method. 3) fully factorise all of the factors of the expression. Once that's completed and the equation has been factorised, the x intercepts can be identified.
Step 1: input integers until x = -1 outputs 0. (Revealing that (x+1) is a factor of the expression.)Step 2: use the 'bus stop' method to get (x+1)(2x^2 - 7x + 3) = 0.Step 3: factorise the polynomial factor to get (2x-1)(x+1)(x-3) = 0.Then identify that x = 1/2, x =-1, and x=3.