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We have that \(3 \cdot f(x) + 4 \cdot g(x) = h(x)\) where f(x), g(x), and h(x) are all polynomials in x. If the degree of f(x) is 8 and the degree of h(x) is 9, then what is the minimum possible degree of g(x)?

 Mar 19, 2020
 #1
avatar+111360 
+2

Multiplying  a  polynomial  by a non-zero constant  does  not  change its degree

 

So    3* f(x)   still has degree  8

 

And  if  h(x)  is  degree 9,  then  g(x)   must  have  degree  9    because

 

Degree  8  + Degree 9    will  result  in a Degree 9  polynomial  = h(x)

 

 

cool cool cool

 Mar 19, 2020
 #3
avatar+389 
+1

Thanks for the help!

qwertyzz  Mar 19, 2020
 #2
avatar+1955 
+2

Nice CPhill!!!!! I want to add on to what you said.

 

If the degree of f(x) is 8, then no matter what x is, the degree will always be 8.

 

g(x) must half a degree 9, which we know thanks to CPhill. A Degree 8 plus Degree 9 will always result in the larger one--- The Degree 9!!! 

 Mar 19, 2020
 #4
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what

Guest Mar 19, 2020

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