(D) To find the remainder when $(3k+2)^2$ is divided by $3$,we expand the expression:$(3k+2)^2 = (3k)^2 + 2(3k)(2) + 2^2$$= 9k^2 + 12k + 4$We can rewr

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(D) To find the remainder when $(3k+2)^2$ is divided by $3$,we expand the expression:$(3k+2)^2 = (3k)^2 + 2(3k)(2) + 2^2$$= 9k^2 + 12k + 4$We can rewrite this as:$= 9k^2 + 12k + 3 + 1$$= 3(3k^2 + 4k + 1) + 1$Since $3(3k^2 + 4k + 1)$ is clearly divisible by $3$,the remainder when the expression is divided by $3$ is $1$.