If $f(x) = 2x^5 - x^4 + x^2 - 3$, and $g(x)$ is a polynomial such that the degree of $f(x) + g(x)$ is 3, then what is the degree of $g(x)$?
+23246 If f(x) is of degree 5 and the sum of f(x) + g(x) is of degree 3, then the degree of g(x) must also be 5.
g(x) = -2x5 + x4 + a·x3+ (don't really care about the x2-term, the x-term, and the consonant; they can be anything) where a is not zero.
If g(x) is created in this way, the fifth-degree term of the sum will disappear as will, also, the four-degree term of the sum, but a third-degree term will remain.
