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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)?

 Jan 23, 2022
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 If b = - 1/2 the first term of g(x) will be - x^14     which will cancel with the x^14  when added with f(x)  leaving degree of 10

 Jan 23, 2022

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