A student is given the following polynomial and is asked to answer questions about it:

x5−198x+5x12+4−2x6
The polynomial contains how many terms?
List all of the coefficients of the polynomial.
What is the polynomial’s constant?
What is the leading coefficient of the polynomial?
What is the degree of the polynomial?

A coefficient is a number stuck to a letter...it HAS to be stuck to a letter to be a coefficient. Our coefficients are 1, -198, 5, and -2 (notice I let out the 4).

That's because a constant is a number NOT stuck to a letter. The 4, then, is the only constant in this polynomial.

The leading coefficient is the number that is stuck to the highest-degree variable. Our highest degree variable is a 12 in 5x^12. So the leading coefficient is 5. In order to have a polynomial in standard form, we always list the terms in order of descending powers (highest power to lowest).

The degree is also the same as the highest power in our polynomial. Ours is a 12th degree.