We have no book and I am trying to go through example problems. I probably need to get a book and learn this all over again. 50 years old no and not done this since 20 years old.
2xsquared-8x+2=0
(2x-2)(1x-1) gets me 4x in the middle when I multiply it through.
Is this the right way to approach this, did I do something silly?
That's because nothing does. You can tell if a quadratic has integer factors by looking at the discriminant,
[tex]\Delta = b^2-4ac = 16-(4)(1)(1) = 12[/tex]. As 12 is not a square number this does not have integer factors and your factorisation is as far as it goes although the 2 can be cancelled