SOLUTION: Suppose f and g are polynomials, and that h(x)=f(g(x))+g(x). Find the degree of g(x) given that the degree of h(x) is 6 and the degree of f(x) is 2.

SOLUTION: Suppose f and g are polynomials, and that h(x)=f(g(x))+g(x). Find the degree of g(x) given that the degree of h(x) is 6 and the degree of f(x) is 2.

Algebra.Com

Question 1038296: Suppose f and g are polynomials, and that h(x)=f(g(x))+g(x). Find the degree of g(x) given that the degree of h(x) is 6 and the degree of f(x) is 2.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since

is degree 2, the degree of

must be 2 times the degree of

. Hence,

must have a degree larger than

. Adding a function to another function of higher degree cannot increase the degree of the higher degree function, hence if

is degree 6, then

must also be of degree 6, and consequently the degree of

must be one half of 6, that is to say, 3.

John

My calculator said it, I believe it, that settles it

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