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 $g(x)$?

Guest Jul 28, 2020

#1**0 **

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) = -2x^{5} + x^{4} + a·x^{3}+ (don't really care about the x^{2}-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.

geno3141 Jul 28, 2020