given that 4x^2-6x+9=A(x-1)(2x+1)+B(x-1)+C for all values of x, find the values of A, B and C

1 answer

just expand the right side and the equate coefficients of like powers. If the polynomials are identical, all the powers of x must have the same coefficients.

You can see right off that the right side will have 2Ax^2+...
So, 4 = 2A and A=2

and so on.
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