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Let f(x) = x^14  - 7x^9 - 3x^2 + 2 and g(x) = 2x^14 + 3x^10 - 6x^8 + 2x - 1.  Let b be a constant.  What is the smallest possible degree of the polynomial f(x) + b*g(x)?

 

If a is the constant the the largest possible degree of is f(x) + a*g(x)?

 Jun 29, 2021
 #1
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Note that if you make b = - 1/2         g(x) becomes   - x^14 - 1.5 x^10 +3 x^8 -x + 1/2   

   when you add this to f(x)   the    x^14  terms will  'cancel out'   and the result is a polynomial of degree  10

 

  For 'a' the largest degree would be   14  

 Jun 29, 2021

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