Quadratic Functions, Equations and Inequalities

The identity\[(2x+a)(x+b)=2x^2+11x+12\] holds for every value of \(x\), where \(a\) and \(b\) are positive integers.

1. Expand the left-hand side and obtain two conditions involving \(a\) and \(b\).

2. Find all possible ordered pairs \((a,b)\). Show why your list is complete.

3. Using your values of \(a\) and \(b\), expand \((2x-a)(x-b)\).