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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)?

 Aug 9, 2021
 #1
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If   a = -1/2          the    x^14  from f(x) and the   2 x^14 from  g(x)  will 'cancel' and you will be left with degree  10  

 Aug 9, 2021

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