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# Question, help me

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

Jul 19, 2019

#1
+2551
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Sorry, I am not experienced in this topic, my answer may be wrong.

In order for f(x) with a degree of 5 to decrease to a degree of 3, g(x) must have a degree of 5 in order to eliminate the degrees of 5 and 4 in f(x).

Jul 19, 2019
edited by CalculatorUser  Jul 19, 2019
#2
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The degree of $$f(x)+g(x)$$ is 3, and the only way that $$g(x)$$ can cancel the term of $$2x^5$$ in f(x) is if $$g(x)$$ contains the term $$-2x^5.$$ Therefore, the degree of $$g(x)$$ is $$\boxed{5}.$$

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Jul 19, 2019
#3
+106533
+2

f(x)  = 2x^5 - x^4  + x^2 - 3

g(x)  =   degree  ???

f(x) + g(x) =   degree 3

The only way  that this is possible  is if   g(x)  = -2x^5 + x^4  + ax^3 +...........

So  g(x)   must be of degree 5

Jul 19, 2019