[tex]2x^2+3x-14[/tex]
We we want to factor this into two brackets, when we multiply the first two terms together we need to get 2x² so the brackets must start with
(2x + ) (x + )
When we times the two end values together we get -14 so the two numbers could be (-14 and 1), (-1 and 14), (-2 and 7), (-7 and 2). The numbers must also add to give +3x.
(2x-14)(x+1) does not work because we end up with -12x when we expand
(2x+14)(x-1) does not work because we end up with +12x when we expand
(2x-7)(x+2) does not work because we end up with -3x when we expand
(2x+7)(x-2) = 2x²+3x-14 therefore this is the correct factorisation.
