Question

If x is natural number which when divided by 5, leaves remainder 3, then the remainder when $x^2-5x+2$ is divided by 5 is

• A. 4
• B. 0
• C. 3
• D. 1

Answer 1

The correct option is D 1

As we know,
$a=bq+r,0\le r<b$
So, we have
$x=5q+3$ [q is the quotient]
Now, putting $x=5q+3$ in $x^2-5x+2$, we get
$(5q+3{)}^2-5(5q+3)+2$
$=25q^2+9+30q-25q-15+2$
$=25q^2+5q-4$
$=25q^2+5(q+1-1)-4$
$=25q^2+5(q-1)+5-4$
$=5(5q^2+q-1)+1$
$=5k+1$ where $k=5q^2+q-1$
So, remainder is 1.
Hence, correct option is d