We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

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 \(f(x) + a\cdot g(x)\)?

 Mar 23, 2019

I assume you may have meant to say smallest, as I have seen those kinds of questions before, so I will answer both.


For largest, because a is a constant, it cannot make the largest exponent any higher, so the answer is 4.


For smallest, we want to cancel some exponents, so we can multiply g(x) by -1/2 and add to get x^4 - 3x^2 + 2 - x^4 + 3x^2 - x + 1/2 = -x + 5/2, so the degree is 1.


Hoping this helped, 


 Mar 23, 2019

12 Online Users