The values of m and n for which the binomial m^3 × n^2 + m^2 × n^5 has a positive value is when m = 3 and n = -1. We can find the answer by substituting the given values in the binomial.
What is a binomial?
A binomial is an equation which consists of two terms connected by a plus or minus sign.
- Substitute m = 3 and n = -1:
[tex]3^3 (-1)^2 + 3^2 (-1)^5\\=27-9\\=18[/tex]
This gives us a positive value.
The remaining don't give positive values.
- Substitute m = -2 and n = -2:
[tex](-2)^3 (-2)^2 + (-2)^2 (-2)^5\\=-32-128\\=-160[/tex]
- Substitute m = -3 and n = -5:
[tex](-3)^3 (-5)^2 + (-3)^2 (-5)^5\\=-625-28125\\=-28750[/tex]
- Substitute m = 1 and n = -2:
[tex]1^3 (-2)^2 + 1^2 (-2)^5\\=4-32\\=-28[/tex]
Thus, the values of m and n for which the binomial m^3 × n^2 + m^2 × n^5 has a positive value is when m = 3 and n = -1. We can find the answer by substituting the given values in the binomial. The correct answer is option A.
Learn more about binomials here-https://brainly.com/question/25982928
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