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Polynomials, SMB-012

.

  1. Show    (1 mark)

  2. Express in the form where is a quadratic factor.  (2 marks)

  3. Justify that only has one zero.  (2 marks)

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i.   

ii.   

iii.   

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i.   .


 

ii.   


 


 

iii.   

Functions, EXT1 F2 2020 HSC 11a

Let  .

  1. Show that  .  (1 mark)

  2. Hence, factor the polynomial    as  , where    is a quadratic polynomial.  (2 marks)

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i.   
   

 

ii.   

Functions, EXT1 F2 2018 HSC 11a

Consider the polynomial  .

  1. Show that    is a zero of  .  (1 mark)

  2. Find the other zeros.  (2 marks)

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i.   

 

ii.   


 

 

 

Functions, EXT1 F2 2007 HSC 2c

The polynomial    has a zero at  . When    is divided by  , the remainder is .

Find the values of    and  .  (3 marks)

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Functions, EXT1 F2 2015 HSC 11f

Consider the polynomials    and  .

  1. Given that    is divisible by  , show that  .  (1 mark)

  2. Find all the zeros of    when  .  (2 marks)

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i.   
 

 

 

ii. 


 

 
 

 

Functions, EXT1 F2 2011 HSC 2a

Let    be a polynomial, where    is a real number.

When    is divided by    the remainder is  .

Find the remainder when    is divided by  .    (3 marks)

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