Answer: Choice A
m = 3 and n = -1
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Step-by-step explanation:
Let's first factor out the GCF
m^3n^2 + m^2n^5
m^2n^2(m + n^3)
The term m^2n^2 is always nonnegative because squaring a negative leads to a positive (eg: (-10)^2 = 100).
So the entire expression is positive when m+n^3 is also positive. In other words when m+n^3 > 0.
If we tried something like m = -2 and n = -2, then,
m + n^3 > 0
-2 + (-2)^3 > 0
-2 + (-8) > 0
-10 > 0
Which is false. So we rule out choice B. You should find that choices C and D lead to similar conclusions. Only choice A works
m + n^3 > 0
3 + (-1)^3 > 0
3 + (-1) > 0
2 > 0
we get a true result here. Note that this happens because the value of m is larger than the absolute value of the result of n^3, which helps keep m+n^3 in positive territory.