Where to find the mod function on ti 89. So I can calculate 14mod 15.

Syntax errors. Check you are inputting your data in the correct order.

The TI-89 does not have a cube root function. However, you can calculate any root simply by raising to the reciprocal of the power. For example, to calculate the cube (third) root of 125, press
5 ^ ( 1 / 3 ) ENTER

Use the catalog.
The CATALOG key is below the APPS key on the TI-89

In Home screen press [F2: Algebra] then select [3:expand(]. The command echoes on main command line. Complete the argument by typing in (x-0.3)(x/2 plus 0.15) and close the right parenthesis of the expand( )function.

You can also use the identity (special product) (a-b)(a plus b)=a^2-b^2. It is not that clear here, but if you you factored out the 1/2 you will see it.
1/2*(x-0.3)(x plus 2*0.15)=1/2*(x-0.3)(x plus 0.3)= 1/2*(x^2-0.3^2)

The function avgRC( calculates forward-difference quotients and the nDeriv( calculates central-difference quotients. Take your pick. You can also use the d( differentiate function.
You can also create a small program or function that gets a function as argument, along with the variable and the step and returns one of the difference quotients. (central, forward, or backward).

If the calculator keeps showing you the same function, you can open the Y= editor and erase the function. To turn calculator OFF, press Diamond key then ON.

Try contacting TI if there was no soluntion in your Operator's Manual.

(a-b)3

The TI-89 has one function to find whatever root you want of a number.

To find the cubed root of say...64, you would type:

root(64,3)

Well the best solution is to stop making more problems