I've got a couple of theorems that I must prove, but I'm completely stumped. Could someone help me out?
- Prove: If P(x) can be divided by Q(x), then it can be divided by cQ(x), where c - any non zero number.
- Prove: If the degrees of P and Q are the same ( equal), then P(x) can be divided by Q(x) then and only then, if Q(x)=cP(x), where c - any non zero number.
- Prove: If c - any non zero number. then polynomials P(x) and cP(x) have the same divisors
I know from simple logic, that they are all true, but I'm bad at writing logic in math proofs.