Yes, it was possible for Jesus to sin. Heb. 4:15 makes this clear when, talking about Jesus (v14), it says:
For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin.
Temptation is the start of the process that leads to sin (James 1:14-15). Jesus was tempted, just like we are — Jesus could have given in to those temptations, if he chose to. Thankfully, he always chose to reject the temptation to sin and, instead, he chose to do the right thing: even though he was tempted he never let it lead him into sin.
One of the wonderful things about this is that it means Jesus can sympathise with us in our weaknesses because he has been through the same kind of experiences (as Heb. 4:15 says above), so he knows how best to help us in our temptations and the trials of life (Heb. 2:17-18).
Now Jesus is immortal (Rev. 1:18), so he can’t be tempted to sin any more (see the answer to Will immortal saints be able to sin?). This is the wonderful hope we have, too.