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?

Answer 1

the answer is c which is 2

Answer 2

The missing exponent on the m-term is 2.

Explanation:

Given : Polynomial
`-2m^2n^3+2m^an^3+7n^2-6m^4`

We have to find the value of a so that when we fully simplified the given polynomial it has degree of 4.

Consider the given polynomial
`-2m^2n^3+2m^an^3+7n^2-6m^4`

Since, given when fully simplified the given polynomial it has degree of 4.

Degree of the polynomial is the highest power of the variables and the sum of exponents that are together.

Since , before simplifying the degree of given polynomial
`-2m^2n^3+2m^an^3+7n^2-6m^4` has degree 5 (
`-2m^2n^3` =2 +3 = 5 )

So , In order to become the polynomial in degree 4 .

The total degree of
`+2m^an^3` has to be 5.

Thus, a+ 3= 5 ⇒ a = 2

Thus, when fully simplify , the given polynomial it has degree of 4.

That is
`-2m^2n^3+2m^2n^3+7n^2-6m^4`

`7n^2-6m^4`

Rearrange in decreasing order of degree, we have,
`-6m^4+7n^2` which is a polynomial of degree 4.