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)?
+1223 \(f(x) + bg(x)\)
\(= (x^4 - 3x^2 + 2) + b(2x^8 - 2x^4 - 6x^2 + 2x - 1)\)
\(= 2bx^8 + (-2b + 1)x^4 + (-6b - 3)x^2 + 2xb + (2-b)\)
If b = 0, then the x^8 term is eliminated, and the smallest possible degree of the polynomial is 4.
