A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions {{MATH_1}} by {{MATH_2}} by cutting out equal squares of side {{MATH_3}} at each corner and then folding up the sides: {{CMD_4}} {{ENV_5}} {{CMD_6}} Express the volume {{MATH_7}} of the box as a function of {{MATH_8}}. {{MATH_9}} {{CMD_10}} {{CMD_11}} Simplify your answer above: {{MATH_12}} {{CMD_13}} {{CMD_14}} What is the (natural) domain of {{MATH_15}}? {{MATH_16}} {{CMD_17}} {{CMD_18}} Is the function {{MATH_19}} a polynomial? {{CMD_20}} {{CMD_21}}yes{{CMD_22}} {{CMD_23}}no{{CMD_24}} {{CMD_25}} {{CMD_26}} {{MATH_27}} is not a polynomial. The domain of a polynomial is {{MATH_28}}. {{MATH_29}} is a polynomial on a restricted domain. {{CMD_30}} {{CMD_31}} {{CMD_32}} Evaluate (either write a number or ``DNE'' (Does Not Exist)): {{ENV_33}} {{CMD_34}} {{CMD_35}} If {{MATH_36}} and increases by {{MATH_37}}, by how much will volume of the box change? Simplify. {{CMD_38}} You may find the following binomial multiplication formulas useful: {{ENV_39}} {{CMD_40}} {{MATH_41}} {{CMD_42}}