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 $f(x) + b\cdot g(x)$?

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When b is a constant (doesn't have any x terms) then it cannot affect the degree of x, so, since the highest degree for both functions is 4 (x^4), it remains at 4.

by Top Rated User (775k points)

Sorry, you're right. The smallest is unchanged, too, at 1, because g(x) has the lowest. Sorry about that.

I'm assuming that constants (degree zero) are not counted as powers of x.

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