[2.23] Try Comdenom() For Faster Partial Factoring - Texas Instruments TI-89 Tip List

Product function ‹() (symbolic)
Iterated multiplication is used for modest numeric limits. Other products are determined by checking
for telescoping products and simple patterns. Limits are used for infinite product limits.
propFrac() (proper fraction)
propFrac() uses polynomial division with remainder to determine the quotient polynomial and the
numerator of the resulting fraction.
solve() (symbolic solve)
solve() uses factoring together with the inverses of functions such as ln(), sin(), etc. Except in exact
mode, these techniques might be supplemented by heuristics to isolate solutions, followed by nSolve()
to refine approximations.
Summation function Σ() (symbolic)
Iterated addition is used for modest numeric limits. Other sums are determined from formulas given in
references such as "Standard Mathematical Tables and Formulae", CRC Press, together with tests for
telescoping sums. Limits or special formulas are used for infinite summation limits.
taylor() (taylor series)
taylor(u,x,n,a) is Σ(limit(d(u,x,k),x,a)*(x-a)^k/k!,k,0,n), computed iteratively to avoid redundant
computation of lower-order derivatives.
tCollect() (trig collect)
tCollect() repeatedly uses the well-known formulas for products and integer powers of sines and
cosines, such as those given in the CRCStandard Mathematical Tables and Formulae.
tExpand() (trig expand)
tExpand() repeatedly uses the well-known formulas for the sine and cosine of multiple angles, angle
sums and angle differences, such as those given in the CRC CRCStandard Mathematical Tables and
Formulae.
zeros()
zeros(expr,var) is expr▶list(solve(expr=0,var),var)

[2.23] Try comDenom() for faster partial factoring

It is not be obvious that comDenom() can be used for factoring, but this is mentioned in the
TI-89/TI-92+ User's Guide, in the Alphabetical Listing of Operations section. As an example, consider
the expression
6 $ x 5 − 8 $ x 4 + 2 $ x 3 2 $ x 3 $ ( x − 1 ) $ ( 3x − 1 )
which can be factored as
To partially factor an expression with comDenom(), include an argument variable which is not in the
expression. I use y in this example:
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