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mathematics UK Year 13 Mathematics (A Levels)
 
Solved problems for the chapter:
 

Synthetic Division of Polynomials

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Zeros of a polynomial for AS level
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:synthetic_division_of_polynomials/4865/


Example 1.

Using the Horner algorithm divide the polynomial




with the following linear polynomials:







    
Example 2.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
3.

Prove that the polynomial is:




divisible by:

  • x + 2

  • x + 3

  • x - 1

    
4.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
5.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
6.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
7.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
8.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    

9.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
10.
Using Horner's algorithm, find the result of the following computational operation between the polynomials:

    
11.

Write the given polynomial as a product of linear and non-linear factors:


    
12.

Write the given polynomial as a product of linear and non-linear factors: