Concept:

Positive integers are those whole numbers which don not contain negative value.

Given:

k² + (k+1)² + (k+2)² to be divided by 3.

And,

k is a positive number.

Find:

We are asked to find remainder.

Solution:

k² + (k+1)² + (k+2)²

First simplify the above expression,

k² + k² + 1 + 2k + k² + 4 + 4k

⇒ 3k² + 6k + 5

We are given that k is positive number,

So, lets, k = 1,

Substitute this value of k = 1 in  3k² + 6k + 5,

We gain,

3k² + 6k + 5

3(1)² +6(1)+5

= 14  

Now, divide 14 by 3, then the remainder will be 2.

Hence, remainder of the given expression is 2.

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Answer:

remainder of the equation is 2 when divided by 3 .

Step-by-step explanation:

Given :- [tex]k^2+ ( k+1)^2 + ( k+2)^2[/tex]

To find :- remainder when the above equation is divided by 3 .

Solution :-

Step 1) given equation needs to be written in simplified form .

Step 2) we will follow the synthetic division approach to divided the equation by 3 .

follow the image solution .

remainder of the equation is 2 when divided by 3 .

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