Let f(x) = x^14 - 7x^9 - 3x^2 + 2 and g(x) = 2x^14 + 3x^10 - 6x^8 + 2x - 1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b*g(x)?
If a is the constant the the largest possible degree of is f(x) + a*g(x)?
+37159 Note that if you make b = - 1/2 g(x) becomes - x^14 - 1.5 x^10 +3 x^8 -x + 1/2
when you add this to f(x) the x^14 terms will 'cancel out' and the result is a polynomial of degree 10
For 'a' the largest degree would be 14
