if the polynomial 2x^2-4x+3 can be expressed in the forma(x-1)(x-2)+b(x-1)+c(x-2), Find the values of a,b and c

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`2x^2-4x+3 = a(x-1)(x-2)+b(x-1)+c(x-2)`

`2x^2-4x+3 = a(x^2-3x+2)+bx-b+cx-2c`

`2x^2-4x+3 = ax^2+(b-3a+c)x+(2a-b-2c)`

Compare components in both sides;

`x^2 rarr 2 = a`

`x rarr -4 = b-3a+c`

`cons. rarr 3 = 2a-b-2c`

`a = 2`

`b-3a+c = -4`

`b+c = -4+6`

`b+c = 2 ----(1)`

`2a-b-2c = 3`

`b+2c = 1 ----(2)`

Solving (1) and (2) will give you;

`b = 3`

`c = -1`

So the answers are a = 2,b = 3 and c = -1

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