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Polynomials

Division

We say D is a factor of P if P = D×Q for some Q.

In this case P/D=Q. .

Determining Q from P/D is usually carried out by long division, a method similar to that for numbers.

Example

(x^3-3*x^2+3*x-1)/(x-1). Write each polynomial with terms in descending powers of x.

The highest term in the numerator is x3. The highest term in the denominator is x.

Start by dividing the highest term in the numerator by the highest term in the denominator, that is, dividing x into x3.

x-1 goes into x^3 - 3*x^2 + 3*x - 1 x^2 - 2x + 1 times

More Examples (this will open in a new window)

Exercise

Compute the polynomial division below. Check your answer when complete.

 
 
P  =  
=   
   

 

If D is not a factor of P, then     P = D×Q + R,      where R is a polynomial of degree smaller than that of D.

Hence, P/D=Q+R/D. .

Example

P=(2*x^2+3*x-1)/(x+1).

x+1 goes into 2*x^2 + 3*x - 1 2*x+1 times with a remainder of 2. So P = 2*x+1 - 2/(x+1).

 

More Exercises (this will open in a new window)

Exercise

Compute the polynomial division below. Write your answer with powers in increasing order and don't type blank spaces in your answer.

 

 =  + 


 

Working space

 

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