Show that (𝑥 − 1) is a factor of 𝑓(𝑥)=2𝑥^3 + 𝑥^2 − 8𝑥+ 5. Hence fully factorise 𝑓(𝑥) fully.

For the show that part of the question simply substitute all the 𝑥's in 𝑓(𝑥) with 1, as the factor 𝑥 − 1 means that 𝑥 - 1 = 0 therefore 𝑥 = 1. Once substituted in solve the equation and show that it is equal to 0 which proves 𝑥 − 1 is a factor of the equation.For the second part use synthetic division to factorise the equation, diving 1 into the equation (with a remainder 0) to produce a quadratic equation which then can be solved through standard factoring. The solution is 𝑓(𝑥) = (𝑥 − 1)(𝑥 + 2)(𝑥 − 1)