## Precalculus (6th Edition) Blitzer

The complete statement is: The degree of the polynomial function $f\left( x \right)=-2{{x}^{3}}\left( x-1 \right)\left( x+5 \right)$ is $5$. The leading coefficient is $-2$.
Consider the polynomial function: $f\left( x \right)=-2{{x}^{3}}\left( x-1 \right)\left( x+5 \right)$ The degree of factor $2{{x}^{3}}$ is 3 and the leading coefficient is $-2$ The degree of factor $\left( x-1 \right)$ is 1 and the leading coefficient is 1. The degree of factor $\left( x+5 \right)$ is 1 and the leading coefficient is 1. Therefore, the degree of $f\left( x \right)$ is $3+1+1$ that is 5 and the leading coefficient is $-2\cdot 1\cdot 1$ that is $-2$ The degree, $n=5$ and the leading coefficient, $-2$. Hence, the degree of the polynomial function $f\left( x \right)=-2{{x}^{3}}\left( x-1 \right)\left( x+5 \right)$ is $5$. The leading coefficient is $-2$.