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1) 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 $f(x) + b\cdot g(x)$?

 

2)Suppose  is a polynomial such that , , , and . What is the sum of the coefficients of ?

 

3)Let  and . Let  be a constant. What is the largest possible degree of ?

 

4)Let  be a quadratic polynomial such that  , and  Let  Find the sum of the coefficients of the terms in  with even exponents. (For example, the sum of the coefficients of the terms in  with even exponents is )

 

Thank you!

 Oct 22, 2020
 #1
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1) if b = -1/2   when yo add the two polynomials together the   4   and the  2  dgrees 'cancel out'   and you are left with degree of one ;     x1

 Oct 22, 2020

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