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# Division of Polynomials by Christopher Monahan

Division of polynomials is very similar to the long division you did in middle school. Consider the process of dividing 5249 by 321:

Because 103 is less than the divisor 321, we have that the quotient is 16 and the remainder is 113. That is, 5249 ÷ 321 is

.

Dividing polynomials is a similar process, but there are places where you will need to be careful. Read through each of the examples that follow. After you have read each problem, copy it onto a piece of paper and see if you can arrive at the correct answer. Be sure to be careful when doing the subtraction.

We find that 6x3 − 7x2 − 47x − 36 by 3x + 4 = 2x2 − 5x − 9.

Finishing the problem, you see that

divided by
is
.

Divide

.

This problem has a remainder, so the solution is

.

Example: Divide 8r3 − 4r2 + 19 by 2r + 3.

Note that there is no term between −4r2 and 19 containing an r. We insert a placeholder, using a 0 for a coefficient. The steps for solving the problem remain the same.

8r3 − 4r2 + 19 divided by 2r + 3 is

.

Divisors do not always have to be binomials.

Example: Divide

by
.

Therefore,

divided by
is
.

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#### THE EVERYTHING GUIDE TO ALGEBRA

By Christopher Monahan

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