Question

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?

Answer 1

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.

Answer 2

Answer:

2

Step-by-step explanation: