Polynomial Algebra 2 proof

Question

A polynomial P is said to be even if P(-x)=P(x) for all x. A polynomial P is said to be odd if P(-x)=-P(x) for all x.
1. Show that if P(x)=ax^4 + bx^3 +cx^2 +dx+e is even, then b=d=0
2. Show that if P(x)=ax^5+ bx^4 +cx^3 +dx^2 +ex+f is odd, then b=d=f=0

Answer 1

If P(x) is even, find P(x) and P(-x).  Set them equal.  Combine like terms.  What is left?