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1. e. If the quadratic 2x^2+bx+6 factorises as (2x+r)(x+s), then r and s must multiply to give 6. As these must be integers, they must be factors of 6.

The pairs of factors that multiply to give 6 are: (2x+3)(x+2), (2x-3)(x-2), (2x+1)(x+6) and (2x-3)(x-2).

The value of b for each of these pairs is: -13, -7, 7 and 13. Therefore these are the values of b that can produce integer factorisations.