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

 

If \(a\) is the constant the the largest possible degree of \(f(x) + a\cdot g(x)\) is \(4\)

 Mar 19, 2020
 #1
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If  b = -1/2  the both the x4 and x2 terms cancel out leaving the x-term; the degree becomes 1.

 

Since a is a constant, the x4 term remains and there is no term with a larger exponent; the degree stays 4.

 Mar 19, 2020
 #2
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Thanks for the help!

qwertyzz  Mar 19, 2020

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