Seeing Structure in Expressions

Directions: What are the maximum and minimum values for c if x^2 + 12x + 32 = (x+a) (x+b) + c? Source: Jedidiah Butler

Directions: Using the digits 1 to 9, at most one time each for a, b, and c, find the result with the greatest and least value: Source: Dane Ehlert

Directions: Fill in the blanks with integers so that the quadratic expression is factorable.   Source: Nanette Johnson