the TI-84 will not do symbolic algebra ... in other words, it will not "factor" a polynomial.
you can graph the polynomial and find its real roots (if it has any).
if at least one of the roots you find is rational, then you can use the factor theorem to attempt a complete factorization of the polynomial.
besides, you don't need a calculator to factor the two cubics you listed.
the first one can be factored by grouping ...
\(\displaystyle \L x^3 - 2x^2 - 9x + 18 =\)
\(\displaystyle \L x^2(x - 2) - 9(x - 2) =\)
\(\displaystyle \L (x - 2)(x^2 - 9) =\)
\(\displaystyle \L (x-2)(x-3)(x+3)\)
the second one is the sum of two cubes ... know the factoring pattern for this situation? ... if not, I recommend you learn it.
\(\displaystyle \L a^3 + b^3 = (a+b)(a^2 - ab + b^2)\)
so ... \(\displaystyle \L x^2 + 64 = x^3 + 4^3 = (x + 4)(x^2 - 4x + 16)\)
:roll: