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can be expressed as a quotient of two linear functions. What is the sum of the elements of \(s\)?

 Dec 21, 2020
 #1
avatar+116126 
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Note that  x^2  + 7x  - 44  can be factored as  ( x + 11) ( x - 4)

 

So  we need  to  see if  x^2 + 5x + a    can be  factored using one - or both  - of  the factors above

 

Note  that if   a  = -36   we have  the factrization  ( x + 9) ( x - 4)

 

And the ratio of linear functions  is   ( x + 9)  / ( x + 11)

 

And  if a    =    - 66   we have the factorization  ( x + 11) ( x - 6)

 

And the ratio of linear  functions is  ( x - 6) / ( x - 4)

 

So  a =  -36   or a =  -66

 

And their  sum is   -102

 

cool cool cool

 Dec 21, 2020

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