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

Factor and remainder theorems

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Zeros of a polynomial for AS level
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Mathematical induction
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:factor_and_remainder_theorems/5467/


Example 1.
   
Example 2.
   
3.

Prove by mathematical induction:




for each

   
4.
Find the number a so that the polynomials are divisible by each other. Write down their quotient.



    
5.
Calculate quotient:

    
6.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
7.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
8.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    

9.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
10.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
11.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
12.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
13.
Check whether the polynomial p (x) is divisible by the polynomial q (x)



    
14.
Find the number a so that the polynomials are divisible by each other. Write down their quotient.



    
15.
Find the number a so that the polynomials are divisible by each other. Write down their quotient.



    
16.

Determine the number a so that the remainder when is divided by is 4. Write the quotient k (x) in this division.