We have that $3 \cdot f(x) + 4 \cdot g(x) = h(x)$ where $f(x),$$g(x),$$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 $g(x)$ ?

Guest Aug 30, 2023

#1**+1 **

\(3 \cdot f(x) + 4 \cdot g(x) = h(x) \)

Multiplication of a polynomial by a non-zero constant doesn't change its degree

If the degree of h(x) is 9, then the minimum degree of g(x) must also be 9 .......since the degree of f(x) is less than 9, it doesn't affect the degree of f(x) + g(x)

CPhill Aug 31, 2023