SOLUTION: How is dividing a polynomial by a binomial similar or different from long division you learned in elementary school? Can understanding how to do one kind of division help you with
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Question 252756: How is dividing a polynomial by a binomial similar or different from long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might uses polynomial division? Found 2 solutions by Greenfinch, Edwin McCravy:Answer by Greenfinch(383) (Show Source):
You can put this solution on YOUR website! Yes, it is very similar. To divide 113724 by 78 you are effectively doing the following
(7 x 10) + (8 x 1) | (1 x 100000) + (1 x 10000) + (3 x 1000) + (7 x 100) + (2 x 10) + (4 x 1)
Substitute X for 10 and you will get
7X + 8 into X^5 + X^4 + 3X^3 + 7X^2 + 2X + 4
The answer to the first is 1458
To the second x^3 + 4X^2 + 5X + 8
Hope that is what you were looking for
If you pick digits very carefully so there is
no carrying to do in any of the multiplications or
any borrowing to do in the subtractions, then you can
create an example of long division of a polynomial
by a binomial which is just like it, by using the digits
as coefficientsl.
Here's an example of long division like we learned
in elementary school that is just like a division
by a binomial.
4233 4x^3 + 2x^2 + 3x + 3
------ ----------------------------
21)88897 2x + 1)8x^4 + 8x^3 + 8x^2 + 8x + 7
84 8x^4 + 4x^3
-- -----------
48 4x^3 + 8x^2
42 4x^3 + 2x^2
-- -----------
69 6x^2 + 9x
63 6x^2 + 3x
-- ---------
67 6x + 7
63 6x + 3
-- ------
4 4
Notice that the coefficients on the right are the same
as the digits in the elementary school division on the
left. The difference is that in elementary school division,
every number is considered to be positive, but that is not
necessary in division of a polynomial by a binomial. Also
the coefficients don't have to be small enough to be digits,
as they are here in the example above, in which I carefully
selected the digits. There is never any carrying or
borrowing to do when dividing a polynomial by a binomial.
Also in elementary school division, sometimes when you try
a certain digit in the quotient it turns out to be too small
or too large and then you have to erase it and make it larger
or smaller as the case may be. This is never required in
division of a polynomial by a binomial. But the two
divisions in all other ways very similar.
Edwin
