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Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of \(f(x) + a\cdot g(x)?\)

 Apr 30, 2021
edited by TheEarlyMathster  Apr 30, 2021
 #1
avatar+2250 
+3

Well, looking at both of them, we see x^4, so the largest is x^4

 

=^._.^=

 Apr 30, 2021
 #2
avatar+203 
+3

Ty! :) 

 

 

One of them says 2x^4... Are you sure thats it?

 Apr 30, 2021
edited by TheEarlyMathster  Apr 30, 2021
 #3
avatar+2250 
+2

I am pretty sure, so hopefully it's right. :))

 

=^._.^=

catmg  Apr 30, 2021
 #4
avatar+795 
+2

Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of f(x) + a(g(x))?

 

Since we are told that a is a constant, and since the coefficient does not matter so a doesn’t matter. We just need to find the degree of f(x), add it by the degree of g(x) [this is because for any a, b, c, d, a^b * c^d = ac ^ (b+d)] . The degree of f(x) is 4 and the degree of g(x) is 4. We found that the degree are both the same, and it is not multiply (which I thought before) so the largest degree is 4.

 

 

laugh

 Apr 30, 2021
 #5
avatar+121048 
+2

As long  as  "a"   is not    -1/2,  the largest degree   is  4

 

 

cool cool cool

 Apr 30, 2021

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