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Suppose $f(z)$ and $g(z)$ are polynomials in $z$, and the degree of $g(z)$ is less than the degree of $f(z)$. If the degree of $f(z)$ is two, what is the degree of $f(z)+g(z)$?

 Aug 2, 2018
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if g(z) is is less than f(z) then no matter what, adding any G(z) will not increase F(z)

thus what ever f(z) is, that is what f(z) + g(z) is

 

example

 

f(z) = x^2

G(z) must equal a function with x(degree 1) or 1(degree 0) or something 

 

x^2 + x +1 is still degree 2

 Aug 7, 2018

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