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 $g(x)$?

Lightning
Jul 26, 2018

#1**+1 **

The only way that f(x) + g(x) is of degree 3 is if the g(x) itself is of degree 5 with the first two terms (written in order of descending powers) being -2x^5 + x^4 and the third term being ax^3....where a is a constant.... [there also might be other terms with degrees < 3 ]

CPhill
Jul 26, 2018