How to prove the following proposition?

Let negl₁ and negl₂ be negligible functions. Then,

1. The function negl₃ defined by negl₃ (n) = negl₁ (n) + negl₂ (n) is negligible.

2. For any positive polynomial p, the function negl₄ defined by negl₄ (n) = p(n)negl1 (n) is negligible.

As the book shows the definition as show below, I did not know where to start.

DEFINITION 3.4 A function f is negligible if for every polynomial p(-) there exists an N such that for all integers n > N it holds that f(n) N it holds that f(n)