Q&A #6096

Teachers' Lounge Discussion: Basic operations on Polynomials

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2006011310:17:27
Subject: Re: Help Please

On 2006010822:05:36, Heather wrote:
>Hi I really need a teacher to explain Division Of Polynomials. My
>teacher does not explain it well at school. 

Suppose someone wanted to divide x^2 + 7x+12 by x+3.

x+3 )x^2 + 7x + 12
     x^2  +3x 
           4x + 12
           4x + 12
                0 (remainder is zero) Ans is x + 4.

This might not stay in alignment.  So what we did is first divide x
int x^2.  It went x times.  Then we multiplied back and got x^2 + 3x. 
We subtract and get 4x and then bring down the 12.  Mulitply back and
get 4x+12.  

The following is added just to help you understand with real numbers
rather than the abstract x.    

10+3 )10^2 + 7(10) + 12
      10^2  +3(10) 
           4(10) + 12
           4(10) + 12
                0 (remainder is zero) Ans is 10 + 4=14

Check: 100 + 70 + 12 =182.  Divide by 13 and the answer is 14. 

Remember that to arrange in descending powers of x.  So if you had 3x
+6 + x^3 you would rearrange to:  x^3 + 0x^2 +3x +6.  Since there is
no x^2 term, we represent it by 0x^2; that is an important step. 

I would suggest that you get a text book and work the examples in the
book.  Take a card to cover up the steps and go through each step one
line at a time.  


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