For this case we have that by definition, a polynomial in its standard form is given by:
![P (x) = ax ^ {n} + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f](https://img.qammunity.org/2020/formulas/mathematics/middle-school/dn5kodnl7k92btrhq3ui621s6hp59p89jz.png)
Where:
a, b, c, d, e, f: They are the coefficients
n, n-1,3,2,1: They are the exponents. The degree of the polynomial is "n" because it is the largest exponent.
x: It is the variable
The given polynomial is:
![4m-2m ^ 4-6m ^ 2 + 9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/1jpnyc424gfjyszmfpof9s2xzzcn2l7ox1.png)
Rewriting it in its standard form:
![P (x) = - 2m ^ 4-6m ^ 2 + 4m + 9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6luwwuidtgni08dueeqyu84dcan9ml4hn1.png)
It is a polynomial of degree 4
ANswer:
![P (x) = - 2m ^ 4-6m ^ 2 + 4m + 9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6luwwuidtgni08dueeqyu84dcan9ml4hn1.png)