Quandaries and Queries
  

 

Question:
Find the HCF and LCM of the polynomials given below. Verify that he productof these HCF and LCM differs from the product of the polynomials, if at all, by a factor of -1

  1. 1-x2 and x3 -1
  2. 1 - x2 and x4 - 1

 
 

 

Hi Charanpal,

Suppose that the problem was numeric rather than algebraic. For example find the HCF and LCM of 15 and -21. The first step would be to factor these integers to get

15 = 3 5 and -21 = -3 7

The HCF is then 3 and the LCM is 3 5 7 = 105. The requested check is

15 -21 = -315 and HCF LCM = 3 105 = 315

Now try your problem 1 above. Factoring gives

1 - x2 = (1 - x)(1 + x) and

x3 - 1 = (x - 1)(x2 + x + 1)

Can you complete the problem?

Penny

  
 

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