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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 2022 HSC 3 MC

Let be a polynomial of degree 5. When is divided by the polynomial , the remainder is .

Which of the following is true about the degree of ?

  1. The degree must be 1.
  2. The degree could be 1.
  3. The degree must be 2.
  4. The degree could be 2.
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♦ Mean mark 51%.

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 2010 HSC 2c

Let  , 

where    is a polynomial and    and    are real numbers.

The polynomial    has a factor of  .

When    is divided by    the remainder is  . 

  1. Find the values of    and  .  (2 marks)

  2. Find the remainder when    is divided by  .     (1 mark)

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i. 

 

 

 

 
 
 

ii. 

 

COMMENT: This question requires a fundamental understanding of the remainder theorem.

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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