Question

find remainder when x^2009 is divided by x^2-5x+6.​

Answer 1

Answer:

$split \: by \:middle \: term$

${x}^{2} - 5x + 6 \\ {x}^{2} - (2x + 3x) + 6 \\ {x}^{2} - 2x - 3x + 6$

x( x-2)-3(x-2)

( x-3 )(x-2)

now put value of x=2 nad x=3

in

x ^2009