If m and n are integers, is 6m2 + 34n ? 18 an even integer? Justify your answer.

Question

What will be an ideal response?

Answer 1

No matter what integers replace m and n in the expression 6m^2 + 34n ? 18, the result will always be
an even integer. To see this, observe that
6m^2 + 34n ? 18 = 2(m^2 + 17n ? 9):
Since products, sums, and differences of integers are integers, m^2 + 17n ? 9 is an integer. Thus
6m^2 + 34n ? 18 can be written as 2 times an integer, and so it is an even integer.