f(x)= 2x^3 -7x^2 + 2x +3. Given that (x-3) is a factor of f(x), express f(x) in a fully factorised form.
We will mainly be using a whiteboard but here are some notes:Is (x-3) is a factor of f(x), then if x=3, f(x) =0. I.e. x=3 is a solution too. If we know x =3 is a solution we can solve the other 2 roots by dividing f(x) by 3.
f(x) dividing by x-3 we get 2x^2 -1x-1 So we have to make that equal to 0. And use trial and error.So for e.g. if x=1 then we get 2x^2 -1x-1 =0. So x=1 is a solution.
Now to find the last solution, divide 2x^2-1x-1 by x-1. We get 2x+1. Making 2x+1 =0 we get x=-0.5
Therefore, x=3,x=1,x=-0.5Hence solution is (x-3), (2x+1), (x-1)
RR
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