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Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^8 - 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)?

 Jan 30, 2022
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\(f(x) + bg(x)\)

\(= (x^4 - 3x^2 + 2) + b(2x^8 - 2x^4 - 6x^2 + 2x - 1)\)

\(= 2bx^8 + (-2b + 1)x^4 + (-6b - 3)x^2 + 2xb + (2-b)\)

 

If b = 0, then the x^8 term is eliminated, and the smallest possible degree of the polynomial is 4.

 Jan 30, 2022

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