1. Let \(f(x) = x^4-3x^2 + 2 \) and \(f(x) = x^4-3x^2 + 2 \). Let \(a\) be a constant. What is the largest possible degree of \(f(x) + a\cdot g(x)\)?

2. Let \(f(x) = x^4-3x^2 + 2\) and \(g(x) = 2x^4 - 6x^2 + 2x -1\). Let \(b\) be a constant. What is the smallest possible degree of the polynomial \(f(x) + b\cdot g(x)\)?

Guest Mar 16, 2019

edited by
Guest
Mar 16, 2019