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)?
If b = - 1/2 the first term of g(x) will be - x^14 which will cancel with the x^14 when added with f(x) leaving degree of 10