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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)?

Guest Dec 4, 2014

Best Answer 

 #1
avatar+86859 
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Mutiplying a polynomial by a constant does nothing to change its degree.  And adding two polynomials of the same degree together  - as long as the "lead" terms don't "cancel" each other - will result in a polynomial of that degree. So...the highest possible degree is four.

 

CPhill  Dec 4, 2014
 #1
avatar+86859 
+5
Best Answer

Mutiplying a polynomial by a constant does nothing to change its degree.  And adding two polynomials of the same degree together  - as long as the "lead" terms don't "cancel" each other - will result in a polynomial of that degree. So...the highest possible degree is four.

 

CPhill  Dec 4, 2014

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