Question

Integer x when divided by 7 leaves a remainder of 4. What will be the remainder when x^2+2x is divided by 7?

Answer 1

Answer:

3

Step-by-step explanation:

This is very easily solved by picking a number for x and solving.

We need a number (x) that leaves a remainder of 4 when divided by x.

Let's start with 7 * 1 = 7

7 divided by 7 leaves a remainder of 0

So, 7 + 4 = 11 divided by 7 would leave a remainder 4.

Thus, our integer (x) is 11

Now, what is $x^2+2x$? When x = 11, this is

$x^2+2x=(11)^2+2(11)=143$

What is 143 divided by 7 with a remainder?

140/7 = 20 (no remainder)

So 143/7 will have "3" as remainder.

Thus, we can conclude the remainder of  $x^2+2x$  when divided by 7 will have remainder of 3 no matter the value of x.