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Find the degree of the polynomial \(-2x^6 + 3x^4 + 8x^3 - 151x + 2\)

 

Let \(f(x) = x^4-3x^2 + 2\) and \(g(x) = 2x^4 - 6x^2 + 2x -1\). Let \(a\) be a real number. What is the largest possible degree of\(f(x) + a\cdot g(x)?\)

 

Let \(f(x) = x^4-3x^2 + 2\) and \(g(x) = 2x^4 - 6x^2 + 2x -1\). Let \(a\) be a real number. What is the smallest possible degree of the polynomial \(f(x) + b\cdot g(x)?\)

 

Let \(f(x) = x^4-3x^2 + 2\) and \(g(x) = 2x^4 - 6x^2 + 2x -1\). What is the degree of \(f(x) \cdot g(x)?\)

 Apr 8, 2023
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The largest possible degree of f(x) + a*g(x) is 8.  The smallest possible degree of f(x) + b*g(x) is 2.

 Apr 8, 2023

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