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(a) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1.  Let a be a constant.  What is the largest possible degree of f(x) + a*g(x)?

 

(b) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1.  Let b be a constant.  What is the smallest possible degree of f(x) + b*g(x)?

 Sep 20, 2021
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The degree of  f(x)+kg(x) will be 5 unless k=0. 

 

If k=0   then   f(x)+kg(x)=f(x)     and so the degree will be 4

 Sep 20, 2021

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