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If $f(x) = 2x^5 - x^4 + x^2 - 3$, and $g(x)$ is a polynomial such that the degree of $f(x) + g(x)$ is 3, then what is the degree of $g(x)$?

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 Jul 28, 2020
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If f(x) is of degree 5 and the sum of f(x) + g(x) is of degree 3, then the degree of g(x) must also be 5.

 

g(x) = -2x5 + x4 + a·x3+ (don't really care about the x2-term, the x-term, and the consonant; they can be anything) where a is not zero.

 

If g(x) is created in this way, the fifth-degree term of the sum will disappear as will, also, the four-degree term of the sum, but a third-degree term will remain.

 Jul 28, 2020

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