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 $f(x) + b\cdot g(x)$?

Question

Let  and . Let  be a constant. What is the smallest possible
degree of the polynomial ?

Answer 1

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.

Comments

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

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