Can someone please explain to me how polynomial division works? The lecture my teacher gave didn't make any sense, nor did the book. I'm supposed to be synthetic division, but it doesn't make sense to me. One of my problems is (9x^3 - 18x^2 - x + 2) / (3x + 1). I can set the problem up, but I dont get what im supposed to do from there. I don't want the answer because the teacher gave it to me to check my work, but I would greatly apreciate it if someone could help me through the steps. Thanks!
Polynomial division
- Thread starter yoda
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We can't replicate the missing classroom instruction within this environment, but there are plenty of resources online. Try using a search engine for lessons on long polynomial division and synthetic division.
Eliz.
Eliz.
saxyjazzchik
New member
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- Nov 29, 2006
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Ok this is going to be hard to explain online so bear with me on this one. Ok so we have this little box rule in our class. So on your paper make a little box in the corner and put this
|
|
____ 9 -18 1 2
________________________________
those go in decending order of the exponents on the variable. So on the bottom of your equation you have 3x+1 so if you se that equal to 0, and get the variable by it's self you will get x=1/3 so that is what you put in your box, so now you have.
|
1/3 |
____ 9 -18 1 2
________________________________
so now you take the 9 and you bring it down.
|
1/3 |
____ 9 -18 1 2
________________________________
9
Then you take the 9 and times it by 1 and divide it by 3 (times by the top of the fraction divide by the bottom) you get 3.
|
1/3 |
____ 9 -18 1 2
3
________________________________
9
You then take the 3 and minus it from the -18 and you get -21
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1/3 |
____ 9 -18 1 2
3
________________________________
9 -21
Then take the -21 and times by the 1 and divide by 3 so you get -7. the plug that in under the one and repeat the process. when you fill in your answer you will adventually get. . .
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1/3 |
____ 9 -18 1 2
3 -7 -2
________________________________
9 -21 -6 0 <<<since you got 0 that means you will have no remainder. so now your answer is
9x^2 - 21x -6 but remember how on the bottom in the orginal problem you had 3x-1. you now need to divide the top by 3, since you did that while doing your synthetic divistion. so your final answer will be. . .
3x^2 - 7x - 2
Hope this helped :]
|
|
____ 9 -18 1 2
________________________________
those go in decending order of the exponents on the variable. So on the bottom of your equation you have 3x+1 so if you se that equal to 0, and get the variable by it's self you will get x=1/3 so that is what you put in your box, so now you have.
|
1/3 |
____ 9 -18 1 2
________________________________
so now you take the 9 and you bring it down.
|
1/3 |
____ 9 -18 1 2
________________________________
9
Then you take the 9 and times it by 1 and divide it by 3 (times by the top of the fraction divide by the bottom) you get 3.
|
1/3 |
____ 9 -18 1 2
3
________________________________
9
You then take the 3 and minus it from the -18 and you get -21
|
1/3 |
____ 9 -18 1 2
3
________________________________
9 -21
Then take the -21 and times by the 1 and divide by 3 so you get -7. the plug that in under the one and repeat the process. when you fill in your answer you will adventually get. . .
|
1/3 |
____ 9 -18 1 2
3 -7 -2
________________________________
9 -21 -6 0 <<<since you got 0 that means you will have no remainder. so now your answer is
9x^2 - 21x -6 but remember how on the bottom in the orginal problem you had 3x-1. you now need to divide the top by 3, since you did that while doing your synthetic divistion. so your final answer will be. . .
3x^2 - 7x - 2
Hope this helped :]