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Part A. Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. Let $a$ be a constant. What is the largest possible degree of $f(x) + a\cdot g(x)$?
Part B. Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. Let $b$ be a constant. What is the smallest possible degree of the polynomial $f(x) + b\cdot g(x)$?

 May 6, 2022
 #1
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A) The largest possible degree of f(x) + ag(x) is 8.

 

B) The smallest possible degree of f(x) + bg(x) is 2.

 May 6, 2022
 #2
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How about putting a little effort into presenting your question properly.

 May 7, 2022

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