How does Macbeth view Banquo, following Duncan's murder?
Macbeth fears Banquo beyond all others, for good reason. First of all, he knows Banquo is brave and capable of acting against him (he "dares" much and has a "dauntless temper of mind"). Then, he knows that Banquo is intelligent enough to get away with whatever he does. He may have the crown, but he does not have security. Banquo's very presence threatens his security, as does the presence of his children. (The wyrd sisters have prophesized that Banquo's children (and grandchildren) will keep the throne). Macbeth may actually begin to hate Banquo at the point where all this hits home: he realizes that he has given his soul for an impermanent temporal prize.
Two good answers - it's also important to note that the failure of the murderers to kill Fleance would aggravate Macbeth's already deteriorating condition. His visions and basic state of mind are clearly affected by the escape of Fleance.
Macbeth knows he must get rid of Banquo and his sons because of the prophecy that Banquo will be the father of many kings. He sees him as a threat to remaining king. He feels he has no choice but to kill him.