|
|
|
|
|
|
|
||
|
|
|
|
|
Polynomial Long Division: Examples (page 3 of 3) Sections: Simplification and reduction, Polynomial long division
This can be done in either of two ways. If you know how to factor quadratics, you can factor the top and then cancel the common factor, like this:
But what if you don't know how to factor? You can always use long division:
(Don't forget to change your signs, as shown in red.) The answer is the polynomial across the top: x + 2
This division did not come out even. What am I supposed to do with the remainder? Think back to when you did long division with plain numbers. Sometimes there would be a remainder; for instance, if you divide 132 by 5:
...there is a remainder of 2. Remember how you handled that? You made a fraction, putting the remainder on top of the divisor, and wrote the answer as "twenty-six and two-fifths":
You do the same thing with polynomial division. Since the remainder is –7 and since the divisor is 3x + 1, then turn this into a fraction and add it (don't multiply it) to the polynomial across the top of the division symbol. Since the division looks like this:
...then the answer is this: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved
Note that there is a gap in the degrees of the terms of the dividend: the first polynomial has no x term. It can get very messy inside the division symbol, so it is very important that you leave space for a x-term column. You can do this by turning the dividend into 2x3 – 9x2 + 0x + 15. Then do the division:
I need to remember to add the remainder to the polynomial part of the answer:
The answer is: Write neatly, remember to change your signs, and work carefully. These problems should not be very hard. Annoying, maybe, but not hard. Just take your time. << Previous Top | 1 | 2 | 3 | Return to Index
|
|
|
|
Copyright © 2006-2008 Elizabeth Stapel | About | Terms of Use |
|
|
|
|
|
|
