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# help plz! ty :D

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

=^._.^=

Apr 30, 2021
#2
+203
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Ty! :)

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

Apr 30, 2021
edited by TheEarlyMathster  Apr 30, 2021
#3
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I am pretty sure, so hopefully it's right. :))

=^._.^=

catmg  Apr 30, 2021
#4
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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(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.

Apr 30, 2021
#5
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As long  as  "a"   is not    -1/2,  the largest degree   is  4

Apr 30, 2021