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

Arithmetic of polynomials

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:arithmetic_of_polynomials/5565/


Example 1.
Calculate the sum and difference of the following two polynomials:



    
Example 2.
Calculate the sum and difference of the following two polynomials:



    
3.
Calculate the sum and difference of the following two polynomials:



    
4.
Find the value of the polynomial using Horner's algorithm:



at


    
5.
Calculate the sum and difference of the following two polynomials:



    
6.
Calculate the product of the following two polynomials:



    
7.

What is the value of the polynomial:




for the following values of x











    
8.
Calculate the product of the following two polynomials:



    

9.
Find the value of the polynomial using Horner's algorithm:



at


.

    
10.
Calculate the product of the following two polynomials:



    
11.
Find the value of the polynomial using Horner's algorithm:



at


.

    
12.
Calculate the product of the following two polynomials:



    
13.
Find the value of the polynomial using Horner's algorithm:



at


.

    
14.
Calculate the product of the following two polynomials:



    
15.
Find the value of the polynomial using Horner's algorithm:



at


.

    
16.
Calculate the given arithmetic operations:













for polynomials






    
17.
Find the value of the polynomial using Horner's algorithm:



at


.

    
18.
Calculate the given arithmetic operations:











for polynomials






    

19.
Find the value of the polynomial using Horner's algorithm:



at values:





    
20.
Find the polynomial if:





and the polynomial is of degree , has a leading coefficient equal to and constant term equal to .

    
21.
Find the polynomial if:





and the polynomial is of degree , the constant term is and the coefficient of the linear term is equal to .

    
22.
Find the polynomial if:







and the polynomial is of degree , the leading coefficient is equal to and the constant term is .

    
23.
Find the polynomial if:





and the polynomial is of degree , has a leading coefficient equal to and constant term equal to .

    
24.
Find the polynomial if:





and the polynomial is of degree , has a leading coefficient equal to , constant term equal to and the coefficient of the linear term is .

    
25.
Find unknowns a, b and c to which the following applies:

    
26.
Find unknowns a, b and c to which the following applies:

    
27.
Find unknowns a, b and c to which the following applies:

    
28.

Given the polynomial:




Identify and write down the:

  • degree of the polynomial,

  • leading term,

  • constant term of the polynomial.

    

29.

The polynomial is given. Calculate the values of and so that the points and lie on the graph of the polynomial.

    
30.

For the polynomial , identify and write down:

  • degree of polynomial,

  • constant term of the polynomial,

  • leading coefficient of the polynomial,

  • .

    
31.

In the given polynomials p and q:






Determine the unknowns , , , and so that the polynomials are equal.