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 $f(x) + a\cdot g(x)$?

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Since a is a constant it cannot change the degree of the polynomial, the highest of which is 4 (because of the x^4 terms).
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