Question

How do you write `2+r-r^3` in standard form and what is the leading coefficients?

Answer 1

Standard form for this polynomial would be: `-r^3 +r +2`, and the leading coefficient is -1

Explanation:

To express a polynomial in standard form, your arrange the terms from highest to lowest degree. The degree of a term is the exponent of its variable. Thus, the degree of our `-r^3` is 3, that of r is 1 (since r is equal to r to the first power), and the degree of the constant 2 is 0 (since there is no variable present). Thus, from highest to lowest we would have `-r^3+r+2`

(Of note, when discussing the degree of a polynomial, we consider the highest degree of the terms in that polynomial to be the polynomial's degree. In this case, that means the polynomial is of 3rd degree.)

The leading coefficient of a polynomial is the first coefficient you see when you put the polynomial in standard form. More formally, the leading coefficient is the coefficient of the highest degree term. In this case, since said term is `-r^3`, the leading coefficient is `-1` (because `-r^3 = (-1)r^3`) .