Answer:
Option (c) is correct.
power of m has to be 2.
Step-by-step explanation:
Given : Polynomial \(-2m^2n^3+2m^{(x)}n^3+7n^2-6m^4\)
We have to find the value of x so that the given polynomial has to be a binomial with a degree of 4 after it has been fully simplified.
Consider the given polynomial \(-2m^2n^3+2m^{(x)}n^3+7n^2-6m^4\)
We call a polynomial a binomial if it has two terms.
And for degree 4 the greatest power of variables in an term must have to be 4.
Thus, for given polynomial to be a binomial with a degree of 4.
The degree of \(-2m^2n^3\) and \(2m^{x}n^3\) has to be same so that they get cancel out and we are left with two terms and \(-6m^4\) will have the highest degree 4.
Thus, power of m has to be 2.
Thus, when power of m is 2 , then
\(-2m^2n^3+2m^{2}n^3+7n^2-6m^4\)
\(\Rightarrow -2m^2n^3+2m^{2}n^3+7n^2-6m^4\)
\(\Rightarrow 7n^2-6m^4\)
Which is a binomial with a degree of 4 after it has been fully simplified.
