(a) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1. Let a be a constant. What is the largest possible degree of f(x) + a*g(x)?
(b) Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^5 - 6x^2 + 4x - 1. Let b be a constant. What is the smallest possible degree of f(x) + b*g(x)?
+128408 a)
Let a be a non-zero constant
A non-zero constant multiplying a polynomial does not change its degree
Since g(x) has degree 5 and f(x) has degree 4, adding them will produce a polynomial of degreee 5
b) If we let b = 0, then g (x) = 0.......so f(x) + b* g(x) will have the degree of f(x) = 4...and this will be the smallest possible degree fo f(x) + g(x)
