Let

Now putting,

A(x-1)²+B(2x-3)(x-1)+C(2x-3) = 5x²-18x+17

Putting x-1=0,

X=1

A(0)+B(0)+C(2-3)=5-18+17

C(-1)=4

Putting 2x-3=0,

A=5

By equating the coefficient of x², we get ,

A+2B=5

5+2B=5

2B=0

B=0

From equation (1), we get,