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Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b \cdot g(x), where f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5 and g(x) = x^6 - 17x^5 + 2x^4 + 6x^3 + 11x^2 - 8x + 1.

 Jun 13, 2024

Best Answer 

 #1
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It is impossible to eliminate both the \(x^5\) term and the \(x^6\) term at once, so we set \(b = 0 \rightarrow f(x) + b \cdot g(x) = f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x + 5\)\(\text{deg}(f(x) + b \cdot g(x) = \boxed{5})\)

 Jun 13, 2024
 #1
avatar+14 
+1
Best Answer

It is impossible to eliminate both the \(x^5\) term and the \(x^6\) term at once, so we set \(b = 0 \rightarrow f(x) + b \cdot g(x) = f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x + 5\)\(\text{deg}(f(x) + b \cdot g(x) = \boxed{5})\)

EquationEnthusiast Jun 13, 2024

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