For which values of m and n will the binomial m^3n^2 + m^2n^5 have a positive value? A) m = 3 , n = -1

B) m = -2 , n = -2

C) m = -3 , n = -5

D) m = 1 , n = -2

^=means exponent

m = 3 and n = -1

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.