"Yet it was said / It should not stand in thy posterity / But that myself should be the root and father / Of many kings... / May they not be my oracles as well, / And set me up in hope?" Macbeth Act 3.1.5-10
Banquo considers the prophecies of the witches. He thinks that since their predictions for what would happen to Macbeth came true, surely their predictions for him to father a long line of kings would hold true as well.
"Tonight we hold a solemn supper, sir, / And I'll request your presence." Macbeth Act 3.1.15-16
Macbeth invites Banquo to a formal supper. He also mentions that Malcolm and Donalbain are still out there and have not been served justice for Duncan's murder.
"He chid the sisters / When first they put the name of king upon me / And bade them speak to him. Then, prophet-like, / They hailed him father to a line of kings. / Upon my head they placed a fruitless crown" Macbeth Act 3.1.62-66
Macbeth also realizes that the witches prophesied a long line of kings for Banquo, not himself. He begins to think that his reign will ultimately become forgotten and meaningless
"And with him / Fleance, his son, that keeps him company, / Whose absence is no less material to me / Than is his father's, must embrace the fate / Of that dark hour." Macbeth 3.1.152-157
Macbeth tells the hired murderers that Banquo must be killed because he can't be trusted. Macbeth also orders the killing of Banquo's family.
Macbeth talks to Lady Macbeth about how he feels uneasy about Banquo. He says "there shall be done / a deed of dreadful note" but doesn't tell her exactly what he plans to do.
"there shall be done / a deed of dreadful note" Macbeth 3.2.
"O treachery! Fly, good Fleance, fly, fly, fly! / Thou mayst revenge-O slave!" Macbeth 3.3.25-26
Banquo is slain by the murderers, but his son is able to escape.