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1. Find the constant a such that (x^2-3x+4)(2x^2+ax+7) = 2x^4-11x^3+30x^2-41x+28

 

2.Suppose that f is a polynomial such that (x-1)*f(x) = 3x^4+x^3-25x^2+38x-17

a. What is the degree of f?

b. What is the leading term of f(x)?

c. What is the constant term of f(x)?

d. Find f(x)

 Aug 1, 2020
 #1
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Find the terms that result in an x^2

 

x^2 *7      +      2x^2 *4     + (-3x)(ax)   =   + 30 x^2

15  x^2   - 3ax^2   = 30 x^2

15 -3a = 30

a = -5

 

 

 

Second one   Just divide   (x-1)   into   3x^4 x^3 -25x^2 + 38x -17    via synthetic or longhand division to find (f(x)

 Aug 2, 2020

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