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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
avatar+703 
+1

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
avatar+102399 
+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

 

cool cool cool

 Jul 19, 2019

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