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.
No he could not have sinned. He is God in the flesh. God cannot sin.
john the baptist said behold the lamb of the world … sacrifical lambs were without spot, wrinkle blemish or any such thing. they were a perfect animal. Christ was a perfect sacrifice.
If we believe for a moment that christ could have sinned we are likening God in a casino hoping to roll double sixes. God takes and took no chances with this serious matter of fulfilling OT prophecy and teaching his children, so HE humbled himself and put on flesh and was tempted because flesh has wants and desires, like us we are also tempted of our flesh.
Gods ways are sure.