pka's not-so-fond memory

pka

pka

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Jan 29, 2005
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AH! Synthetic Division that is not so fond memory from my childhood.
I don't think that it has crossed my path in at least fifty years.
I thought that had gone the way of finding the square root by hand. Guess not.
Have these math-ed types heard of Computer Algebra Systems?
 
It’s still used as a fairly quick calculation of a polynomial’s value, f(a), using the remainder theorem to determine rational roots or bounds for roots that are not rational.

I know that any CAS does a nifty job with less headache.

My not-so-fond memory is reducing matrices to row-echelon form by hand ... one arithmetic error spells doom.
 
pka said:
… I don't think that [synthetic division] has crossed my path in at least fifty years … Have these math-ed types heard of Computer Algebra Systems?
Click to expand...
I regularly see homework exercises containing a synthetic division component (both high school and undergraduate). Perhaps, those schools teach paper-and-pencil methods first (eg: University of Washington).

A couple examples of paper-and-pencil assignments that I haven't seen in a long time are (1) using continued fractions to evaluate square roots and (2) using Descartes' Rule of Signs to obtain information about polynomial roots. (I think Dr Peterson has posted about Descartes' rule recently, though.)

skeeter said:
My not-so-fond memory is reducing matrices to row-echelon form by hand …
Click to expand...
How come you got to stop at REF! Yes, I can remember smoldering annoyance of showing RREF steps written out for larger systems having some rational coefficients, like 5/17 and 11/23 (for Pete's sake).

I like reducing matrices by hand, when demonstrating my own examples.

?
 
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