Math: polynomial long division
The tutor shows an example of how to divide a polynomial by a binomial.
Long division with polynomials is appreciated by math teachers, but few others. What follows is an illustrated example of how to do it.
A simple polynomial long division might begin like this:
The process starts with the question, “How many times does x (from the divisor) go into x2?” The answer is x, and is written on top, above x2:
Next, the x you just wrote on top is multiplied by the divisor; the product is written below the polynomial:
Subsequently, subtraction is done, then the next term (in this case, 7) is brought down:
Now, the process restarts, with the question, “How many times does x go into -x (the result of the subtraction)?” The answer, -1, is written on top, above the column that contains the -x. Afterwards, the -1 is multiplied to the divisor, and the result is written below:
Subtraction is the next step:
The quotient is x-1, the remainder, 5. If the division is correct,
(x-1)(x-2) + 5 should equal x2 -3x + 7
Let’s check:
(x-1)(x-2) + 5 = (using FOIL) x2 -2x -x + 2 + 5
Simplifying gives
x2 -3x + 7
Apparently, this long division was successful.
There is yet more to discuss about polynomial long division. Look for more in coming posts:)
Source:
Travers, Kenneth, et al. Using Advanced Algebra. Toronto: Doubleday Canada Limited, 1977.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.
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