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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 3, 2021
 #1
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if b = - 1/2      the   x^14 terms will 'cancel out'    leaving degree 10

 

  No matter WHAT constant 'a' equals, the degree will never be greater than 14

 Aug 3, 2021

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