When P(x) is divided by x^2-3x+2 the remainder is 4x-7. Find the remainder when P(x) is divided by x-1 and x-2

P(x) = k*(x^2 - 3x + 2) + 4x-7

= k*(x-1)*(x-2) + 4x-7

now the first term is divisible by (x-1) and (x-2). So just check for remainder when (4x-7) is divided by (x-1) and (x-2)
=> 4x-7 = 4(x-1) -3 ........> remainder = -3

=> 4x-7 = 4(x-2) + 1.........>remainder = 1

(x-1)(x-2) = x^2 -3x + 2,

so if you divide P(x) by this, then the remainder is still 4x-7

x^2 -3x + 2 = (x-1)(x-2)