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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 $8$ and the degree of $f(x)$ is $4$.

 Oct 8, 2017
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"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 8 and the degree of f(x) is 4."

 

f(x) = a*x4 + b*x3 + ...

 

g(x) = c*xn + d*xn-1 + ...

 

h(x) = a*(c*xn + d*xn-1 + ...)4 + b*(c*xn + d*xn-1 + ...)3 + ... + c*xn + d*xn-1 + ...

 

h(x) = a*c4*x4n + ....

 

Must have 4n = 8  hence n = 2

 

Degree of g(x) is 2.

 Oct 8, 2017

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