>Long division is exactly the process one uses when dividing one polynomial
>by another.
Yes, in outline they are the same; but there are serious disanalogies
between polynomial and decimal whole number division.
The main analogy (as I used to try to teach it to my students) is: digits
are coefficients and powers of the variable are place values, powers of 10.
The disanalogy is: In polynomial division, the coefficients and the powers
of the variable never 'interact'; in decimal whole number division, the
digits and the powers of ten may interact. For example,550 divided by 25
is 22; i. e.
(5 times10^2 + 5 times 10) divided by (2 times 10 + 5) is 2 times 10 + 2;
but (5x^2 + 5x) divided by (2x + 5) is 2.5x - 3.75 + 18.75/(2x + 5).
Try teaching developmental math students that these two problems are solved
by "exactly the [same] process." It really is simpler just to teach
polynomial division (with due reference to the "subtract multiples of the
divisor from the dividend" outline).
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