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-term? 0 1 2 4

Answer 1

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.