Kathy, a standard trick to do this type of question is to eliminate the expressions term by term or to compare coefficients.

Here, eliminating expressions will be good.

Setting x = 1 (x - 1 = 0) eliminates A and B, leaving you to find C.

Setting x = 0 eliminates B, leaving you to find A.

Setting x = some other number helps you
to find the last unknown B.

In recent days I have reduced my frequency of answering posts heavily due to the presence of other helpful tutors and the fact that I have become busier in recent days. You can continue to post questions as usual and someone will answer them. If I have the time to spare, then I will write up my version of the answers.

Got other method?

A second method is to expand everything fully like one of the tutors have done and then comparing terms, but you need to be careful of expanding the brackets.

A third method is very similar to the second, but does not require expansion. This is done at the expense of the prerequisite of strong observation. For example, A must be 2 because the only way we can get the x^3 out is from the (x - 1)^3 term. B and C can be obtained by other methods including my first method.

Actually C can also be found easily because Bx (x - 1) will not contain a constant term. Only the A (x - 1)^3 and the C can spew out the constant terms, but we have found A already. Finding B afterwards is straightforward.

The best way is still to let x = 1, x = 0 and x = 2.

I need help on the last chapter
Are u free

You can post as usual first, but I will appear online at random timings.

The earlier you post, the earlier someone gets to see the question and answer them and if I chance upon the question when I am suddenly free, I can attempt it