+0  
 
0
69
1
avatar

Problem 1)

Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 +x^2 - 7. What is the coefficient of x^3 in the sum f(x) + g(x)?

 

 

Problem 2a)

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)?

 

Problem 2b)

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 • g(x)?

Guest Mar 17, 2018
Sort: 

1+0 Answers

 #1
avatar+6945 
+2

Problem 1)

f(x)  =   x3 + 3x2 + 4x - 7

g(x)  =  -7x4 + 5x3 + x2 - 7

 

We only need to look at the  x3  terms.

 

x3  +  5x3  =  6x3     so the coefficient of  x3  in  f(x) + g(x)  is  6 .

 

Problem 2)

f(x)  =  x4 - 3x2 + 2

g(x)  =  2x4 - 6x2 + 2x - 1

 

a)

The largest possible degree of  f(x) + a * g(x)  is just  4 .

 

b)

If  b  =  -1/2 , then the  x4  terms cancel and the  x2  terms cancel in  f(x) + b * g(x)  so the degree would be  1 .

hectictar  Mar 17, 2018

32 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details