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.