Why bother with Chamber of Secrets' polyjuice plot when you can turn invisible?

Question

Until almost the end of Chamber of Secrets, it's as if Harry has forgotten that he owns an invisibility cloak. There's numerous occasions in the book where it appears to me that using the cloak was either a viable enough option to merit a mention, or just plain better than what they actually did. None of the examples stand out to me more than the polyjuice plot. Many of its risks are discussed in the book (e.g. immense rule-breaking), lots goes wrong when they actually do it, there's clear evidence that they didn't think it through (why steal the targets's shoes but leave your own on when you drink the potion?), and worst of all, it takes an extremely long time to brew the potion, meaning that they've risked lives to make this effort.

This gives me my question - why not just use the cloak? It's a proven effective tool that doesn't have a paper trail, unlike this potion that could well be a deadly botch. All that Harry had to do was put the cloak on, follow a known Slytherin to their common room, and stand and wait until you hear the suspect open his mouth in the presence of his friends. The only advantage that I can think of for the polyjuice plot is that they can use their disguise to guide the conversation towards the subject of interest, but that pales in comparison to the time constraint, the difficulty of finding and fooling Malfoy, and the time wasted searching for the common room. And while we're on this topic, why not use both polyjuice and the cloak? i.e. Do both plots? They didn't even consider using the cloak when they had to steal the ingredients for the potion!

Answer 1

Hermione addresses this point directly. They don't just need to spy on Malfoy, they need to interrogate him.

‘All right,’ said Hermione coldly. ‘What we’d need to do is to get inside the Slytherin common room and ask Malfoy a few questions without him realising it’s us.’

‘But that’s impossible,’ Harry said, as Ron laughed.

‘No, it’s not,’ said Hermione. ‘All we’d need would be some Polyjuice Potion.’

‘What’s that?’ said Ron and Harry together.

‘Snape mentioned it in class a few weeks ago –’

‘D’you think we’ve got nothing better to do in Potions than listen to Snape?’ muttered Ron.

‘It transforms you into somebody else. Think about it! We could change into three of the Slytherins. No one would know it was us. Malfoy would probably tell us anything. He’s probably boasting about it in the Slytherin common room right now, if only we could hear him.’

Additionally, they don't just want answers to one question, they want to get at all of his schemes.

‘I want to know how he fixed that Bludger,’ said Hermione darkly.

‘We can add that to the list of questions we’ll ask him when we’ve taken the Polyjuice Potion,’ said Harry, sinking back onto his pillows. ‘I hope it tastes better than this stuff …’

[later]

The holidays would be the perfect time to use the Polyjuice Potion and try to worm a confession out of him.

Obviously they could hang around Malfoy for a few days or weeks under the cloak in the hopes that he'll say something untoward but the risks of getting caught (tripped over, for example) outweigh the chances of getting the evidence they need.