There are several ways we can solve such identities. We use the fact that the corresponding coefficients of each power of x are equal and the fact that the identity works for any value of x to solve this question.

You have these ideas, where you can use them alone or in combination with one another:
1. Substitution of suitable values of x
2. Comparing coefficients after full expansion
3. Other techniques perhaps?

This question has three unknowns a, b and c. Even if you do not know other techniques, you can still solve them. For three unknowns a, b and c, we need a minimum of three equations to solve them simultaneously.

Just letting x = 2, x = 3 and x = 4 would already give you the three equations needed.

Well, x = 1 would be a slightly better guess to begin with because you obtain the value of c instantly.

For the other two unknowns a and b, we can just let x = 2 and x = 3 to obtain two simultaneous equations.

Or, you can expand the expression fully from the start. Or, do the question in a similar way to the one I have shown in the photo workings.