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(a) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1.  Let a be a constant.  What is the largest possible degree of f(x) + a*g(x)?

 

(b) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1.  Let b be a constant.  What is the smallest possible degree of f(x) + b*g(x)?

 Mar 14, 2021
 #1
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a) 

 

Let  a  be a non-zero constant

 

A non-zero constant  multiplying a polynomial  does  not  change its degree

 

Since  g(x)  has  degree 5  and  f(x)  has degree 4, adding them  will produce a polynomial of  degreee 5

 

 

 

b)  If we let  b  =  0,  then g (x)   = 0.......so   f(x)  + b* g(x)   will have  the degree of f(x)   = 4...and this will  be the smallest possible degree fo  f(x) + g(x)

 

 

 

cool cool cool

 Mar 14, 2021

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