# How do you find the degree and leading coefficient of the polynomial 14b-25b^6?

Jan 14, 2017

Degree of polynomial: $6$
Leading coefficient: $- 25$

#### Explanation:

The degree of a polynomial expression is the largest degree of any term in the polynomial.

The degree of a term is the sum of the exponents of the variable factors of the term.

In this case
$\textcolor{w h i t e}{\text{XXX}} 14 b = 14 {b}^{\textcolor{b l u e}{1}}$ has degree $\textcolor{b l u e}{1}$
$\textcolor{w h i t e}{\text{XXX}} - 25 {b}^{\textcolor{b l u e}{6}}$ has degree $\textcolor{b l u e}{6}$
So the degree of the polynomial is $\textcolor{b l u e}{6}$

To determine the leading coefficient, it is first necessary to write the expression in standard form. This means that the expression should be written with the terms in descending degree sequence.
Therefore the given expression in standard form would be:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{- 25} {b}^{6} + 14 b$
The leading coefficient is the constant factor of the first term (when the expression is in standard form).
Therefore the leading coefficient is $\textcolor{g r e e n}{- 25}$