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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)?

 Mar 17, 2018
 #1
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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 .

 Mar 17, 2018

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