For the polynomial –2m2n3 + 2m?n3 + 7n2 – 6m4 to be a binomial with a degree of 4 after it has been fully simplified, which must be the missing exponent on the m in the second term?
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Answered by
8
Given the polynomial:
-2m^2n^3 + 2m^{\boxed{x}}n^3 + 7n^2 - 6m^4−2m
2
n
3
+2m
x
n
3
+7n
2
−6m
4
where x is the missing exponent.
We desire our polynomial to be a binomial (have two terms) after simplification.
We observe that the first and second term are positive and negative of almost the same term.
Therefore, we rewrite the polynomial in such a way that the first and second term cancels out.
This is:
\begin{gathered}-2m^2n^3 + 2m^{\boxed{2}}n^3 + 7n^2 - 6m^4\\$Simplified, we have:\\\\=7n^2 - 6m^4\end{gathered}
Therefore, the missing exponent on the m in the second term is 2.
Answered by
2
Answer:
2
Step-by-step explanation:
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