How to Divide Polynomials

By Eric Mains
Dividing polynomials is pretty simple once you understand a few basic concepts.
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Rumor has it that the polynomial was invented by an insane math teacher, who created the polynomial as part of his mad quest for a math formula that was utterly indivisible. Had he succeeded, the world might be a poorer place. Learning how to divide polynomials is pretty easy once you get the handle on a couple of basic concepts. Check them out in action on the following polynomial division problem: x^2 + 13x + 42 divided by x + 7 Note: The "^" symbol means that the following number is an exponent.

Step 1

Write down the expressions involved, and name them for easy reference. The polynomial expression that you are trying to divide corresponds to the numerator of a fraction, which is the top number of a fraction. The expression you are using to divide the numerator corresponds to the denominator of a fraction, which is the bottom number of the fraction.

Step 2

Cancel out the first factor in the polynomial equation you are trying to divide. In the example, to cancel out the x^2 in the numerator you need to multiply the entire denominator by x. This gives you x^2 + 7x. Subtract this from the numerator to cancel out the first factor. In the example, the x^2 is cancelled out, and the 13x is reduced to 6x. The 42 is unchanged, leaving a total remainder of 6x + 42.

Step 3

Cancel out the next remaining factor in the numerator. In the example, multiplying the denominator by six results in 6x + 42. When this is subtracted from the remainder, this results in zero.

Step 4

Continue in a similar manner until you have cancelled out all of the factors in the polynomial.

Step 5

Add up the factors you used to cancel out the factors of the polynomial. In the example, you used x and positive six, making the answer to this problem x + 6.

About the Author

Eric Mains has written professionally since 2006, and has been a freelancer since day one. He attended Iowa State University and majored in English with a concentration in linguistics.