We have that $3 \cdot f(x) + 4 \cdot g(x) = h(x)$ where $f(x),$ $g(x),$and $h(x),$ are all polynomials in $x$. If the degree of $f(x)$ is 8 and the degree of $h(x)$ is 9, then what is the minimum possible degree of $g(x)$?
Correct me if I am wrong, but I am pretty sure that g(x) must have a minimum degree of 9.
\(3f(x) = 3a_8x^8+3a_7x^7+...+3a_1x+3a_0\\ 4g(x) = \quad ?\\ h(x) = b_9x^9+b_8x^8+b_7x^7+...+b_1x+b_0\)
If we are adding the polynomials together, then the only way to get a variable to the power of 9 is if g(x) is of degree 9, at a minimum. Note that multiplication does not affect the degree of the polynomial in any way, so we might as well ignore it for the most part.