Show that (π₯ β 1) is a factor of π(π₯)=2π₯^3 + π₯^2 β 8π₯+ 5. Hence fully factorise π(π₯) fully.
For the show that part of the question simply substitute all the π₯'s in π(π₯) with 1, as the factor π₯ β 1 means that π₯ - 1 = 0 therefore π₯ = 1. Once substituted in solve the equation and show that it is equal to 0 which proves π₯ β 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 π(π₯) = (π₯ β 1)(π₯ + 2)(π₯ β 1)
CB
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