Question

If x is a natural number which when divided by 5,
leaves remainder 3, then the remainder when
x2 - 5x + 2 is divided by 5 is
(1) 4
(2) O
(4) 1
(3) 3​

Answer 1

To Find: x, a natural number

Step-by-step explanation:

Lets take as $x^{2}$ square ($x^{2}$)

Then,

x is divided by 5 and leaves a remainder 3

x=5k+3  for some integer  k .

$x^{2}$ − 5x+2

$(5k+3)^{2}$ − 5(5k+3) + 2

=> $25k^{2}$ + 30k + 9 − 25k − 15 + 2

=> $25k^{2}$ + 5k − 4 = ($25k^{2}$ + 5k − 5) + 1

=> 5($5k^{2}$ + k − 1) + 1

=> 5n+1,

where n = $5k^{2}$ + k − 1 (an integer)

So, the Remainder is 1