We have that 3*f(x) + 4*g(x) = h(x) where f(x), g(x) and h(x) are all polynomials in x. If the degree of f(x) is 3 and the degree of h(x) is 5, then what is the minimum possible degree of g(x)?

Guest Jun 26, 2021

#1**+1 **

Multiplying a polynomial by a constant does not change its degree. So 3 * f(x) has the same degree as f(x).

4 * g(x) has the same degree as g(x) adding 3 (fx) + 4 (g(x) will not change the degree of the resulting h(x)

if h(x) is degree 5 then g(x) must be at least degree 5 .

ElectricPavlov Jun 26, 2021