Polynomial functions

1. A certain type of candle is packaged in boxes that measure 36 cm by 15 cm by 8 cm. The candle company that produced the above packaging has now designed shorter candles. A smaller box will be created by decreasing each dimension of the larger box by the same length. The volume of the smaller box will be at the most 930 cm3 . What are the maximum dimensions of the smaller box?

2. Given that 2 5 is a factor of the polynomial function () = 2 + 3, determine the ratio : in simplest form.

3. When ax^3 - x^2 + 3x + b is divided by x - 2, the remainder is 59. When it is divided by x + 1, the remainder is -1. Find the values of a and b.

4. Given () = 3 3 + 2 + 18 8, determine the value of such that (3x - 4) is a factor of f(x).