In theory, I know who the Pharisees and Sadducees are. I’m aware that they were the religious leaders of the time. However, I decided that I needed more info, because I wanted to know the reason why they were called a brood of vipers.

The word Pharisee comes from a Hebrew word meaning separate. A sect that seems to have started after the Jewish exile. In addition to OT books the Pharisees recognized in oral tradition a standard of belief and life. They sought for distinction and praise by outward observance of external rites and by outward forms of piety, and such as ceremonial washings, fasting, prayers, and alms giving; and, comparatively negligent of genuine piety, they prided themselves on their fancied good works.

They held strenuously to a belief in the existence of good and evil angels, and to the expectation of a Messiah; and they cherished the hope that the dead, after a preliminary experience either of reward or of penalty in Hades, would be recalled to life by him, and be requited each according to his individual deeds.

In opposition to the usurped dominion of the Herods and the rule of the Romans, they stoutly upheld the theocracy and their country’s cause, and possessed great influence with the common people. According to Josephus they numbered more than 6000. They were bitter enemies of Jesus and his cause; and were in turn severely rebuked by him for their avarice, ambition, hollow reliance on outward works, and affection of piety in order to gain popularity.

Mat 15:2 Why do thy disciples transgress the tradition of the elders? for they wash not their hands when they eat bread.
Mat 15:3 But he answered and said unto them, Why do ye also transgress the commandment of God by your tradition?

Mar 7:8 For laying aside the commandment of God, ye hold the tradition of men, [as] the washing of pots and cups: and many other such like things ye do.
Mar 7:9 And he said unto them, Full well ye reject the commandment of God, that ye may keep your own tradition.
Mar 7:10 For Moses said, Honour thy father and thy mother; and, Whoso curseth father or mother, let him die the death:
Mar 7:11 But ye say, If a man shall say to his father or mother, [It is] Corban, that is to say, a gift, by whatsoever thou mightest be profited by me; [he shall be free].
Mar 7:12 And ye suffer him no more to do ought for his father or his mother;
Mar 7:13 Making the word of God of none effect through your tradition, which ye have delivered: and many such like things do ye.

And here, Paul was talking about himself as a former Pharisee:

Gal 1:13 For ye have heard of my conversation in time past in the Jews’ religion, how that beyond measure I persecuted the church of God, and wasted it:
Gal 1:14 And profited in the Jews’ religion above many my equals in mine own nation, being more exceedingly zealous of the traditions of my fathers.

The Pharisees were strictly a sect. A member was chaber (united) and was obligated to remain true to the principles of Pharisaism.

Jdg 20:11 So all the men of Israel were gathered against the city, knit together as one man.

They were moral, zealous, and self-denying, but self-righteous and destitute of the sense of sin and need.

Luk 7:39 Now when the Pharisee which had bidden him saw [it], he spake within himself, saying, This man, if he were a prophet, would have known who and what manner of woman [this is] that toucheth him: for she is a sinner.

Luk 18:9 And he spake this parable unto certain which trusted in themselves that they were righteous, and despised others:
Luk 18:10 Two men went up into the temple to pray; the one a Pharisee, and the other a publican.
Luk 18:11 The Pharisee stood and prayed thus with himself, God, I thank thee, that I am not as other men [are], extortioners, unjust, adulterers, or even as this publican.
Luk 18:12 I fast twice in the week, I give tithes of all that I possess.
Luk 18:13 And the publican, standing afar off, would not lift up so much as [his] eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner.
Luk 18:14 I tell you, this man went down to his house justified [rather] than the other: for every one that exalteth himself shall be abased; and he that humbleth himself shall be exalted.

Sadducees = “the righteous”
1) a religious party at the time of Christ among the Jews, who denied that the oral law was a revelation of God to the Israelites, and who deemed the written law alone to be obligatory on the nation, as the divine authority. They denied the following doctrines:
a) resurrection of the body
b) immortality of the soul
c) existence of spirits and angels
d) divine predestination, affirmed free will

They were the religious rationalizers of the time.

Mar 12:18 Then come unto him the Sadducees, which say there is no resurrection; and they asked him, saying,
Mar 12:19 Master, Moses wrote unto us, If a man’s brother die, and leave [his] wife [behind him], and leave no children, that his brother should take his wife, and raise up seed unto his brother.
Mar 12:20 Now there were seven brethren: and the first took a wife, and dying left no seed.
Mar 12:21 And the second took her, and died, neither left he any seed: and the third likewise.
Mar 12:22 And the seven had her, and left no seed: last of all the woman died also.
Mar 12:23 In the resurrection therefore, when they shall rise, whose wife shall she be of them? for the seven had her to wife.

Act 23:8 For the Sadducees say that there is no resurrection, neither angel, nor spirit: but the Pharisees confess both.

They were strongly entrenched in the Sanhedrin priesthood.

Act 4:1 And as they spake unto the people, the priests, and the captain of the temple, and the Sadducees, came upon them,
Act 4:2 Being grieved that they taught the people, and preached through Jesus the resurrection from the dead.

Act 5:17 Then the high priest rose up, and all they that were with him, (which is the sect of the Sadducees,) and were filled with indignation,

The Sadducees are identified with no affirmative doctrine, but were mere deniers of the supernatural.