Question

Find the remainder when x^100 is divided by (x-1)(x-2).

Answer 1

Step-by-step explanation:

$because \: \: its \: divide \: by \: a \: \: quadratic \: \: \\ so \: \: remainder \: is \: \: ax + b \\ \\ {x}^{100} = q(x)(x - 1)(x - 2) + ax + b \\ \\ x = 1 \\ \\ 1 = a + b \: \: \: \: \: \: \: \: \: \: ..........(1) \\ \\ x = 2 \\ \\ {2}^{100} = 2a + b \: \: \: \: \: .........(2) \\ \\ by \: \: (1) - (2) \\ \\ a = {2}^{100} - 1 \\ \\ b = 1 - ( {2}^{100} - 1) = 2 - {2}^{100}$