Factorise 2(x^2) +7x+3

Only factors of 2 are 1 and 2, therefore solution will take form of (2x + a)(x + b) to get 2x² term. Only factors of 3 are 1 and 3 therefore a and b are either 1 or 3. Playing around and intuition leads us to conclude that a=1 and b=3, hence we get:
(2x + 1)(x + 3) which equals 2x² + 7x +3, as 32x + 1x = 7x.